Question 1208101
<pre>
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&1/3}}} 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(1,3, 40/70, "=", (1&1/3)/C)}}}
                                       {{{matrix(1,3, 4/7, "=", (4/3)/C)}}} ---- Reducing left-side fraction, and converting
                                                      right-side numerator to an improper fraction
                                      {{{matrix(1,3, 4C, "=", 7(4/3))}}} -- Cross-multiplying
                                      {{{matrix(1,3, 4C, "=", 28/3)}}}
Number of cups of chocolate chips needed for 70 cookies, or {{{highlight_green(matrix(1,11, C, "=", (28/3)/4, "=", (28/3)(1/4), "=", (7cross(28)/3)(1/cross(4)), "=", 7/3, "=", highlight(matrix(1,3, 2&1/3, "(CHOICE", "d)"))))}}}</pre>