+ — =¢
x —
MATH THAT MAKES
¢ ENTS
worksheet 5 - lemonade anyone?
GRADE
5
Jose and Nick decide to sell lemonade on a hot summer day. They’re selling two sizes: a 25-cent
cup and a smaller 10-cent cup. At the end of the day, they’ve made $8.45.
They count the number of empty cups remaining. They started out with equal numbers of large and
small cups, but now have three more small cups than large.
How many cups of each size lemonade did they sell?
If they spent $1.25 on the cups, $1.50 on the lemons and the sugar was free from Jose’s parents
kitchen, how much did they earn selling lemonade? Was it worth it?
MATH STANDARDS ALIGNMENT:
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based
on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy
to a written method and explain the reasoning used.
Personal Finance Big Ideas:
What is Money, Cost/Benefit Analysis, Time Value of Money
METHOD 1: GUESS, TEST, & REVISE (OR HYPOTHESIZE, TEST, & REVISE)
I’m going to make a table with values of small and large cups that are three apart, then see when I get the right total.
To do this, I’ll have to multiply the small by 0.10 (ten cents) and the large by 0.25 (a quarter).
small small * .1 large large * .25 total
10
1
13
3.25
$4.25 much too small!
20
2
23
5.75
$7.75 closer
25
2.5
28
7.00
$9.50 too much!
22
2.2
25
6.25
$8.45 just right!
My first guess was way too small, so I doubled it. This still wasn’t enough, but it was much closer, so I just added 5
more. This was way too much, so I went more than half way back - to 22, which was just right. If it hadn’t been, I would
have tried 21 or 23 for the number of smaller cups, depending on what the results were.
They spent $1.25 on the cups, $1.50 on the lemons, so in total they spent:
$1.25 + $1.50 = $2.75
Since they had $8.45 at the end of the day, the total they earned was $8.45 take away the cost of their supplies,
$2.75.
$8.45 + $2.75 = $5.70
Nick and Jose made $5.70 selling lemonade. I think it was worth it because that was more than they spent on the
supplies and they probably had fun.
1
MATH THAT MAKES CENTS
+ — =¢
x —
MATH THAT MAKES
¢ ENTS
GRADE
5
worksheet 5 - lemonade anyone?
METHOD 2: LOGICAL REASONING
Since there were 3 more large cups sold than small cups, I subtracted $.75 from the total made (3 * .25 = $.75). The
result was $7.70.
This value, $7.70, is what they would have had if an equal number of small and large cups had been sold. Therefore,
this number must be divisible by $.35, the sum of the prices (large + small = $.25 + $.10).
$7.70 divided by $.35 is 22, so there were 22 small cups sold and 25 large cups sold.
To figure out what they earned selling lemonade, I can just subtract the cost of their supplies from the total they made.
$8.45 - $1.50 - $1.75 = $5.70. They earned $5.70.
I think it was not worth it because that is not very much money. Maybe they should have charged more per cup and
made more money.
METHOD 3: ALGEBRAIC
Let’s call the number of large cups l and the number of small cups s. Since I know there were 3 more large cups sold
than small cups, I can use my variables to say:
l=s+3
I also know that each large cup sold for 25 cents and each small cup sold for 10 cents. Since I know that the total was
$8.45, I can use my variables to say:
0.25 l + 0.10 s = 8.45
I can substitute my first equation in to my second for l to get the following:
0.25 (s + 3) + 0.1 s = 8.45
Now I distribute to begin simplifying the equation, combine like terms, then divide to find the value of s:
0.25 s + 0.75 + 0.1 s = 8.45
0.35 s = 7.7
s = 22
So there were 22 small cups sold and 25 large cups sold (s + 3).
They earned $5.70, I know because I subtracted the cost of the lemons and the cups from the total they made $8.45 –
($1.50 + $1.25) = $5.70.
I think it was only worth it if they had nothing else to do that day and no other way to make more money. If they could
have done something else to make more money that day (mow laws, babysit, rake leaves, sell their toys) then they
could have been making more money and so it would not really be worth it.
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MATH THAT MAKES CENTS