Question

Henry is making a corn grits recipe that calls for 1/4 cup of corn grits for every 1/2 cup of water. How much water will he need if he uses 1 1/2 cups of corn grits?

Answer 1

Method 1:

$\begin{array}{ccc}\dfrac{1}{4}\ \text{cup of corn}&-&\dfrac{1}{2}\ \text{cup of water}\\\\1\dfrac{1}{2}=\dfrac{3}{2}\ \text{cup of corn}&-&x\ \text{cup of water}\end{array}\qquad\text{cross multiply}\\\\\\\dfrac{1}{4}\cdot x=\dfrac{3}{2}\cdot\dfrac{1}{2}\\\\\dfrac{1}{4}x=\dfrac{3}{4}\qquad\text{multiply both sides by 4}\\\\\boxed{x=3}$

Answer: Henry will need 3 cups of water.

Method 2:

$\begin{matrix}\dfrac{1}{4}\ \text{cup of corn}&-&\dfrac{1}{2}\ \text{cup of water}&|\text{multiply both sides by 2}\\\\\dfrac{1}{2}\ \text{cup of corn}&-&1\ \text{cup of water}&|\text{multiply both sides by 2}\\\\1\ \text{cup of corn}&-&2\ \text{cup of water}&|\end{matrix}$

$\begin{matrix}\left(\dfrac{1}{2}+1\right)\ \text{cups of corn}&-&(1+2)\ \text{cups of water}\\\\1\dfrac{1}{2}\ \text{cups of corn}&-&3\ \text{cups of water}\end{matrix}$

Answer: Henry will need 3 cups of water.

Answer 2

The ratio is 0.25:0.5

If he uses 1.5 cups of corn grits, the ratio is multiplied by 6.

So:

1.5 : 3.0

He will need 3 cups of water.