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Define a variable, used let statements, set up an equation, then solve. Morgan is making two cookie recipes. Recipe A calls for one-third third less than twice the number of cups of sugar that Recipe B calls for. If she needs four and one-sixths cups of sugar in all, how many cups will she need for Recipe A?

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EXPLANATION

Let's see the facts:

-Morgan is making ----------------> 2 cookie recipes.

Recipe A ---> A = 2RecipeB -(1/3) 2RecipeB

-She needs-----------> Recipe A + Recipe B = 4 1/6 cups of sugar

Now, we have a system of equations:

(1) A = 2B -(1/3)2B

(2) A + B = 4 1/6

Multiplying both sides of (1) by 3:

3A = 6B - B

Simplifying:

3A = 5B

Isolating B:

B = 3/5 A

Substituting B-value in (2)

[tex]A\text{ + }\frac{3}{5}A\text{ = 4}\frac{1}{6}[/tex]

Reordering:

[tex]A+\frac{3}{5}A=\text{ }\frac{25}{6}[/tex]

Multiplying both sides by 30:

[tex]30A\text{ + 18A = 25}\cdot5[/tex][tex]48A\text{ = 125}[/tex]

Dividing both sides by 48:

[tex]A\text{ = }\frac{125}{48}[/tex]

Representing as mix fraction and rounding:

[tex]A=\text{ 2}\frac{2}{3}[/tex]

ANSWER: She will need two and two-thirds cups of Recipe A.