# Question #5d65c

Jul 25, 2017

1) $\frac{3}{2}$ or $1 \frac{1}{2}$cups

2) $6$ cups are required

#### Explanation:

1) To double the recipe, we are asking to double the amount of sugar (thus making two batches). To do this, we simply multiply $\frac{3}{4}$ by $2$:

$\frac{3}{4} \times 2 \to \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = \frac{3}{2}$cups or $1 \frac{1}{2}$cups

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2) We can set up the following equation:

$\frac{3}{4} c = 4 \frac{1}{2}$

Where:

$> \frac{3}{4}$ is the amount of sugar needed to make one batch of cookies

$> c$ is the amount of $\cup s$

$> 4 \frac{1}{2}$ is how many batches we want to bake

Here, we are simply solving for $c$,

$\frac{3}{4} c = \frac{9}{2}$ (Notice how I changed $4 \frac{1}{2}$ into an improper fraction)

Cross Multiply:

$\text{Top Left" times "Bottom Right"="Top Right" times "Bottom Left}$:

$2 \cdot 3 c = 9 \cdot 4$

$6 c = 36$

Divide $6$ to both sides:

$\frac{\cancel{6}}{\cancel{6}} = c = \frac{36}{6}$

$c = 6$

Thus we need $6$ cups of sugar if we are to make $4 \frac{1}{2}$ batches of cookies.