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

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.

Answer 2

Method 1:

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

Answer: Henry will need 3 cups of water.

Method 2:

`\begin{matrix}(1)/(4)\ \text{cup of corn}&-&(1)/(2)\ \text{cup of water}&|\text{multiply both sides by 2}\\\\(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((1)/(2)+1\right)\ \text{cups of corn}&-&(1+2)\ \text{cups of water}\\\\1(1)/(2)\ \text{cups of corn}&-&3\ \text{cups of water}\end{matrix}`

Answer: Henry will need 3 cups of water.