SOLUTION: A math assessment question I need to understand. Logan is making chocolate chip cookies. He found a recipe that makes 40 cookies and calls for 1 and 1/3 cups of chocolate chips

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Question 1208101: A math assessment question I need to understand.
Logan is making chocolate chip cookies. He found a recipe that makes
40 cookies and calls for 1 and 1/3 cups of chocolate chips. If he
wants to make 70 cookies, which equation correctly calculates how
many cups of chocolate chips Logan will need?
a). 1 and 3/4 x 1 and 1/3 = 15/12 = 1 and 1/4 cups
b). 1 and 1/2 x 1 and 1/3 = 12/6 = 2 cups
c). 1 and 4/7 x 1 and 1/3 = 44/21 = 2 and 2/21 cups
d). 1 and 3/4 x 1 and 1/3 = 28/12 = 2 and 1/3 cups
Found 3 solutions by josgarithmetic, MathTherapy, math_tutor2020:
Answer by josgarithmetic(39616) About Me  (Show Source):
Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
A math assessment question I need to understand.

Logan is making chocolate chip cookies. He found a recipe that makes
40 cookies and calls for 1 and 1/3 cups of chocolate chips.  If he
wants to make 70 cookies, which equation correctly calculates how 
many cups of chocolate chips Logan will need?

a). 1 and 3/4 x  1 and 1/3 = 15/12 =  1 and 1/4 cups
b). 1 and 1/2 x  1 and 1/3 = 12/6  =  2 cups
c). 1 and 4/7 x  1 and 1/3 = 44/21 =  2 and 2/21 cups
d). 1 and 3/4 x  1 and 1/3 = 28/12 =  2 and 1/3 cups

You can set this up as a PROPORTION.
As given, 40 cookies require 1%261%2F3 cups of chocolate chips
Let the amount of cups of chocolate chips needed for 70 cookies, be C
We then get the following PROPORTION: matrix%281%2C3%2C+40%2F70%2C+%22=%22%2C+%281%261%2F3%29%2FC%29
                                       matrix%281%2C3%2C+4%2F7%2C+%22=%22%2C+%284%2F3%29%2FC%29 ---- Reducing left-side fraction, and converting
                                                      right-side numerator to an improper fraction
                                      matrix%281%2C3%2C+4C%2C+%22=%22%2C+7%284%2F3%29%29 -- Cross-multiplying
                                      matrix%281%2C3%2C+4C%2C+%22=%22%2C+28%2F3%29
Number of cups of chocolate chips needed for 70 cookies, or

Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: choice D

Explanation

The recipe Logan found yields 40 cookies.
He instead wants 70 cookies.
70/40 = 7/4 = 1 & 3/4 is the ratio or scale factor we need to apply to scale up the recipe.

As a simpler example, let's say he wanted to make 80 cookies. That means he'd need to double each portion since 80/40 = 2.
Or if he wanted 120 cookies, then he needs to triple each ingredient since 120/40 = 3.
And so on.

Anyways back to 1 & 3/4.
Based on this value, the answer is between choices A and D.

1 & 3/4 = 7/4
1 & 1/3 = 4/3
(7/4)*(4/3) = (7*4)/(4*3) = 28/12 = 7/3 = 2 & 1/3

The result 28/12, along with 2 & 1/3, point us to choice D as the final answer.

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Another approach would be to use a calculator
(7/4)*(4/3) = 2.3333... where the 3's go on forever.
This matches with 2 & 1/3 = 2 + (1/3) = 2 + 0.3333... = 2.3333...

which helps confirm that the answer is choice D