Question

Carly is making three cakes for the bake sale. the second cake requires 1/2 cups more flour than the first cake the third cake requires twice the amount of flour as the first cake the two pound bag of flour she bought has 8 1/2 cups exactly the she needs how much flour is needed for each cake.

Answer 1

First cake requires x cups of flour.
Second cake: x + 1/2
Third cake: 2x

2 pound bag has 8 1/2 cups and it's exactly what Carly needs, so we can write it down as:

8 1/2 = x + x + 1/2 + 2x
8 1/2 = 2x + 1/2 + 2x
8 1/2 = 4x + 1/2                    / - 1/2 (both sides)
8 = 4x                                   / ÷ 4 (both sides)
x = 2

Doublecheck:

2 + 2 + 1/2 + 2 * 2 =
= 2 + 2 + 1/2 + 4 =
= 4 + 1/2 + 4 =
= 8 + 1/2 =
= 8 1/2

It's the same, so it must be correct ;)

Answer: Carly needs 2 cups of flour for each cake.