CPM Homework Help : PC Problem 1-134

Tiffani has a craft business that is expanding and she plans to cut down on expenses by purchasing craft paints in bulk. Most of them are straight mixtures, except for vibrant green, which she mixes specially. To create the mixture, she mixes one pint of the standard green paint with one teaspoon of red and two teaspoons of yellow. She has one pint of red and two pints of yellow paint that she wishes to add to the green paint to create the special mix. How many gallons of the green paint will she need in order to use all of her red and yellow paint? Below is a list of the equivalent measures.

$\text{one gallon}=128\ \text{ounces}$

$\text{one ounce}=6\ \text{teaspoons}$

$\text{one pint}=16\ \text{ounces}$

$\text{one pint}=2\ \text{cups}$

Step 1:

Calculate the number of batches of paint one pint of red could make.

Hint:

What about the yellow paint?

Step 2:

Now, calculate the number of batches one gallon of green paint will make.

Answer 1:

$\left(\frac{\text{6 teaspons}}{\text{ounce}}\right)\left(\frac{\text{16 ounces}}{\text{pint}}\right)=96\text{ batches}$

Answer 2:

It would be the same number of batches since you have twice as much yellow paint but the amount needed is twice as much as the red.

Answer 3:

There are 4 quarts to a gallon. Each quart has 2 pints. So you can make 8 batches of the special green with one gallon of the standard green.Now set up a proportion and solve.

Partial Answer:

$\frac{1\ \text{gallon\ green}}{8\ \text{batches}}= \frac{x\text{\ number\ of\ gallons\ of\ green}}{96\text{\ batches}}$