brain archive

Problem

If Evan made $64 on Monday and he made one quarter of that amount on Tuesday, how much did he make on Tuesday?

Answer

Math Strategy Used: Write an equation.

64 x 1/4 = 16

Evan made $16 on Tuesday.

Problem

One day, a man goes to a horse race. Instead of counting how many people and horses are at the race, he counts the number of heads and the number of legs. There are 74 heads at the race and 196 legs. How many people and how many horses were at the race?

Answer

Math Strategies Used: Write two equations and solve using variables.

(This is a very tricky problem that requires you to use variables and solve for two equations. Don't worry if you're not quite ready to do this math!)

Let's say that x equals the number of humans at the horse race.

Let's say that y equals the number of horses at the horse race.

We know that x + y = 74 (because each human and each horse has one head, right?)

And we know that 2x + 4y = 196 (because each human has 2 legs and each horse has 4 legs)

So our two equations are

x + y = 74 and
2x + 4y = 196

Now solve the first equation for y.

x + y = 74 means that
y = 74 – x

If that's true, then we can substitute (74 - x) for y in the second equation and solve for x:

2x + 4y = 196 means that
2x + 4(74 – x) = 196 means that
2x + 296 – 4x = 196 means that
2x – 4x = –100 means that
–2x = –100 means that
x = 50

So there are 50 people at the horse race. (Remember x equals the number of people.)

Now solve the first equation for y. We know that x = 50, so

50 + y = 74 means that
y = 24

There are 50 people at the horse race and 24 horses. Well done!

Problem

Evan earned $32 on Monday. On Tuesday and Friday, each day, he earned 17 times as much money as he did on Monday. How much money did he earn in all?

Answer

Math Strategies Used: Make an organized list and Write an equation.

How much did Evan earn on Monday? 32

How much did Evan earn on Tuesday? 32 x 17 = 544

How much did Evan earn on Wednesday? 32 x 17 = 544

32 + 544 + 544 = 1120    Evan earned $1,120 all together.

Evan definitely won the Lemonade War this time around!

Problem

On Monday, Zeke puts 3 ice cubes in each of his 84 cups of lemonade. On Tuesday, he puts 4 ice cubes in each of his 63 cups of lemonade. How many ice cubes did Zeke use?

Answer

Math Strategy Used: Write an equation.

3 x 84 = 252    Zeke used 252 ice cubes on Monday.

4 x 63 = 252    Zeke used 252 ice cubes on Tuesday.

252 + 252 = 504    Zeke used 504 ice cubes all together.

Wow! That's a lot of ice!

Problem

Mallory and Maci are each having a lemonade stand. Mallory has 20 cups. It takes her two minutes per cup to make the lemonade and fill each cup. Maci has 12 cups. Her cups are bigger than Mallory's. It takes Maci five minutes per cup to make the lemonade and fill each cup. How many minutes will it take Mallory to fill all of her cups? Maci? Who will spend the most time filling her cups?

Answer

Math Strategy Used: Write an equation.

20 x 2 = 40    It will take Mallory 40 minutes to fill her cups.

12 x 5 = 60    It will take Maci 60 minutes to fill her cups.

Maci will spend the most time filling her cups.

Problem

Jackie has $7. Matt has $5. How much would they have together if Matt had $50?

Answer

Math Strategy Used: Write an equation.

7 + 50 = 57

They would have $57 together IF Matt had $50. But he doesn't!

Problem

Once upon a time, there were 60 cups of lemonade. Along came 40 more cups of lemonade. How many cups of lemonade are there now?

Answer

Math Strategy Used: Write an equation.

60 + 40 = 100

There are now 100 cups of lemonade.

Problem

Carly has $276 from selling cars. JoJo has $20 more than Carly, but Cal has $50 less than Carly. How much money do the three friends have all together?

Answer

Math Strategy Used: Write an equation.

276 (Carly has $296.)

276 + 20 = 296 (JoJo has $296.)

276 – 50 = 226 (Cal has $226.)

276 + 296 + 226 = 798

The three friends have $798 all together.

Problem

Jessie has 200 dollars. She gives 80 dollars to Megan, and she gives 30 dollars to Evan. How much money does Jessie have now?

Answer

Math Strategy Used: Write an equation.

200 – 80 = 120 (Now Jessie has $120.)

120 – 30 = 90 (Now Jessie has $90.)

Jessie has $90 now.

Problem

Jenny has 6 loaves of bread. She gives her friend 1-1/2 loaves. Then she gives another friend 3-1/4 loaves. How much bread does Jenny have left?

Answer

Math Strategies Used: Write an equation, Solve a simpler problem, and Draw a picture.

First, draw a picture using boxes to represent each loaf of bread. There are six loaves of bread, so we draw 6 boxes. Imagine the last loaf of bread divided in half.

Take away 1-1/2 loaves of bread. How many are left?

6 – 1-1/2 = 4-1/2 (or four and a half loaves of bread).

Now divide that leftover half loaf of bread in half again. (one half = two quarters)

Take away 3-1/4 loaves of bread. How many are left?

4-1/2 – 3-1/4 = 1-1/4 (or one and a quarter loaves of bread).

Jenny now has 1-1/4 loaves of bread.

Problem

Shane had $100. He spent $23.32. Then he spent $56. Then someone gave him $78. How much money does Shane have now?

Answer

Math Strategies Used: Write an equation.

100 – 23.32 – 56 + 78 = 98.68.

Shane now has $98.68.

Problem

Max has $51.99. He gives seven cents to Mason, and he gives $21.78 to Megan. How much do Mason and Megan have together? How much does Max have now?

Answer

Math Strategies Used: Solve a simpler problem and Write an equation.

There are two problems here. First:

0.07 + 21.78 = 21.85.

Mason and Megan have $21.85 together.

Second:

51.99 – 21.85 = 30.14.

Max now has $30.14.

Problem

Casey and her little sister Bella had a contest to see who could sell the most lemonade. Their mom bought 60 cups and divided them evenly between the two girls. When the contest was over, Casey sold all but 2 of her cups of lemonade for $1.50 per cup, and 3 of her customers came back for refills. (When a customer gets a refill, he or she uses the SAME cup.) Meanwhile, Bella sold all of her cups of lemonade, but no one came back for a refill. She sold her lemonade for $1.45 per cup. Who filled the most cups of lemonade? Who sold more cups? Who made the most money?

Answer

Math Strategies Used: Solve a simpler problem, Write an equation, and Construct a table.

There are SIX problems here, three for Casey and three for Bella. As we solve each problem, we will put the answer in the following table:

Each girl begins the day with 30 cups. (60 ÷ 2 = 30)

CASEY, PROBLEM 1

Casey starts the day with 30 cups.
Casey ends the day with 2 cups.

30 – 2 = 28 cups filled.

CASEY, PROBLEM 2

Casey sells 28 cups of lemonade.
Casey sells 3 refills of lemonade.

28 + 3 = 31 cups of lemonade sold.

CASEY, PROBLEM 3

Casey sells 31 cups of lemonade.
Each cup sells for $1.50.

31 x 1.50 = 46.50 dollars earned by Casey.

Ready for Bella's problems now?

BELLA, PROBLEM 1

Bella starts the day with 30 cups.
Bella ends the day with 0 cups.

30 – 0 = 30 cups filled.

BELLA, PROBLEM 2

Bella sells 30 cups of lemonade.
Bella sells 0 refills of lemonade.

30 + 0 = 30 cups of lemonade sold.

BELLA, PROBLEM 3

Bella sells 30 cups of lemonade.
Each cup sells for $1.45.

30 x 1.45 = 43.50 dollars earned by Bella.

So, let's take a look at our completed table and answer each question.

Who filled the most cups of lemonade?

Bella filled the most cups of lemonade. (30 cups filled)

Who sold the most cups of lemonade?

Casey sold the most cups of lemonade. (31 cups sold)

Who made the most money?

Casey earned the most money. ($46.50 earned)

Problem

A girl buys 55 cans of lemonade. Each can makes 24 ounces of lemonade. The girl fills each cup that she sells with 4 ounces of lemonade. In the end, she sells 320 cups of lemonade! How many cups of lemonade could she have sold if she had used all the lemonade she bought? How many cups of lemonade were left over?

Answer

Math Strategies Used: Solve a simpler problem and Write an equation

There are TWO problems here:

PROBLEM 1

A girl bought 55 cans of lemonade.
1 can makes 24 ounces of lemonade.

55 x 24 = 1,320 ounces of lemonade.

The girl has 1,320 ounces of lemonade.
1 cup holds 4 ounces of lemonade.

1,320 ÷ 4 = 330 cups of lemonade.

The girl could have sold 330 cups of lemonade.

PROBLEM 2

The girl had 330 cups of lemonade.
She sold 320 cups of lemonade.

330 – 320 = 10 cups.

She had 10 cups of lemonade left over.

Problem

Sela bought 100 cups for a lemonade stand. She charged 50 cents per cup of lemonade sold. She made 34 sales of lemonade, but 3 of those sales were to people who came back for refills. (HINT: If you buy a refill and use the same cup, you still have to pay for the lemonade.) How much money did Sela raise? How many cups were used? How many cups were left over?

Answer

Math Strategies Used: Solve a simpler problem and Write an equation

There are THREE problems here:

PROBLEM 1

Sela sold 34 cups of lemonade.
3 cups were refills.

34 – 3 = 31 cups.

Sela used 31 cups.

PROBLEM 2

Sela bought 100 cups.
Sela used 31 cups.

100 – 31 = 69 cups.

Sela had 69 cups left over.

PROBLEM 3

Sela sold 34 cups of lemonade.
Each cup of lemonade cost 50 cents.

34 x 50 = 1700 cents = $17

Sela made $17 selling lemonade.

Problem

Evan went to the store and bought fifty cups. The next day, he had a lemonade stand and used 21 of those cups to sell lemonade for 50 cents per cup. Five of the cups he sold had refills, which means the customer bought a second cup of lemonade but used the same cup. How many cups did Evan have left at the end of the day? How much money did Evan make selling lemonade?

Answer

Math Strategies Used: Solve a simpler problem, Make an organized list, and Write an equation

There are TWO problems here:

PROBLEM 1

Evan had 50 cups.
Evan used 21 cups.

50 – 21 = 29 cups.

Evan had 29 cups left at the end of the day.

PROBLEM 2

Evan sold 21 cups of lemonade.
Evan sold 5 refills of lemonade.
Each cup of lemonade cost 50 cents.

21 + 5 = 26 lemonade sales.
26 x 50 = 1300 cents = $13

Evan made $13 selling lemonade.

Problem

Evan has five dollars, and his best friend Paul has forty-six dollars. How much money do they have together?

Answer

Math Strategies Used: Write an equation

Evan has 5 dollars.
Paul has 46 dollars.

5 + 46 = 51 dollars.

Sounds like they're ready for a trip to the Big Dipper ice cream shop!

Problem

Imagine you start your lemonade stand with 1,959 cups of lemonade. You sell 42 cups of lemonade, but then 7 cups are returned to you because they have bugs in them. Ew! How many cups of lemonade do you end up with (including the buggy ones that are returned to you)?

Answer

Math Strategies Used: Make an organized list and Write an equation

You start with 1,959 cups.
You sell 42 cups.
You get back 7 cups.

So 1,959 – 42 + 7 = 1,924 cups of lemonade.

That's a lot of lemonade!

Problem

How many friends helped Evan sell lemonade during the Lemonade War?

(Ooh, this problem is tricky. You have to read the book to answer it!)

Answer

Math Strategies Used: Make an organized list and Write an equation

Here are the friends who helped Evan:

Scott Spencer
Paul
Jack
Ryan

So 1 + 1 + 1 + 1 = 4! Four friends helped Evan sell lemonade during the Lemonade War.

Problem

Evan and Scott decide to sell lemonade every day for a whole week (except for Monday). Every day, except for Monday, they sell 45 cups of lemonade. They charge 50¢ for each cup. How much money do they have at the end of the week? If they split the money evenly, how much money does each one make?

Answer

Math Strategies Used: Make an organized list and Write an equation

On Sunday, they sell 45 cups
On Monday, they sell 0 cups
On Tuesday, they sell 45 cups
On Wednesday, they sell 45 cups
On Thursday, they sell 45 cups
On Friday, they sell 45 cups
On Saturday, they sell 45 cups

So all together, Evan and Scott sell 270 cups of lemonade.
(45 + 45 + 45 + 45 + 45 + 45 = 270)

They sell each cup of lemonade for 50¢, so every time they sell 2 cups they make a dollar. How many groups of 2 are there in 270?

270 ÷ 2 = 135

So Scott and Evan earn $135 by the end of the week.

They split their earnings evenly: Evan gets half and Scott gets half. How much is half of $135?

$135 ÷ 2 = $67.50

Evan and Scott each get $67.50 at the end of the week. Wow! That's a lot of lemon loot!

Problem

If Evan makes $110.10 selling lemonade, and Jessie makes $60.49 selling lemonade, how much more money will Evan make?

Answer

Math Strategies Used: Write an equation

110.10 – 60.49 cents = 49.61

Evan will make $49.61 more selling lemonade than Jessie does.

Problem

If Jessie starts out with $50, and then she sells 60 cups of lemonade at 50¢ each, how much money will she have all together?

Answer

Math Strategies Used: Write an equation

60 cups x 50 cents = 3000 cents, which equals $30

So, Jessie will have $30 after she sells the lemonade. Now, add that money to the $50 she already had:

$30 + $50 = $80

Jessie will have $80 all together.

Problem

If Jessie and Megan earn $30 selling lemonade each day for three days in a row, and Megan has an extra $10 to add to their earnings, will they have enough money to win the Lemonade War?

Answer

Math Strategies Used:Make an organized list and Write an equation

Day 1 they earn $30

Day 2 they earn $30

Day 3 they earn $30

Megan has an extra $10

So...$30 + $30 + $30 + $10 = $100.

Jessie and Megan will have $100, which is enough to win the Lemonade War. (Remember, Evan had just $62.11 at the end of the five days.)

Problem

If Evan has 60 cups of lemonade and he sells each cup for $1.50, how much money will he make if he sells all of the lemonade?

Answer

Math Strategies Used: Write an equation

60 cups x $1.50 = $90.

Evan will make $90 if he sells all of the lemonade.

Problem

If Evan had 8 pitchers of lemonade and each pitcher gives out 8 cups, how much money will he make if he sells each cup for 50 cents?

Answer

Math Strategies Used: Solve a simpler problem and Write an equation

1. How many cups of lemonade does Evan have?

Evan has 8 (pitchers) x 8 (cups) = 64 cups of lemonade.

2. How much money will he make?

64 cups x $0.50 = $32.

Evan will make $32 if he sells all of the lemonade.

Problem

Evan is organizing a basketball tournament on the school playground. He needs to put five kids on each team. Twenty-two kids show up to play. How many teams can he organize? Are there any kids leftover? If so, how many?

Answer

Math Strategies Used: Draw a picture and Write an equation

Draw 22 X's on the page. Group the X's in rows of 5.

X X X X X = 5 kids = 1 team

X X X X X = 5 kids = 1 team

X X X X X = 5 kids = 1 team

X X X X X = 5 kids = 1 team

X X = two kids leftover

Evan can organize 4 teams with 2 kids leftover.

22 ÷ 5 = 4, remainder 2

Problem

Jessie has $3.67 in her lockbox, all in coins. She has twice as many quarters as she has dimes. She has the same number of nickels as she has dollar bills. She has one more penny than she has dimes. How many dollar bills, quarters, dimes, nickels, and pennies does Jessie have?

Answer

Math Strategies Used: Make an organized list and Guess and check

Okay, first, we know that Jessie has no dollar bills because the problem tells us that the money is all in coins. That means she has no nickels either.

Dollar bills 0
Quarters
Dimes
Nickels 0
Pennies

Now, let's make a guess. Let's guess that she has eight quarters. That would mean she has four dimes. How much money does that equal? Eight quarters equals two dollars and four dimes equals forty cents. Hmm. That's only $2.40. Not enough money. Let's guess again.

Let's guess she has twelve quarters. That would mean she has six dimes. How much money does that equal? Twelve quarters equals three dollars and six dimes equals sixty cents. Hey! That's $3.60, which is just seven cents less than the total amount of $3.67. If Jessie has seven pennies, that's one more penny than she has dimes (6 dimes). So we can fill in the rest of our list and then check our answer again:

____________________________

TOTAL = $3.67

Good job!