Question

Arnie is mixing red and yellow paints to make two different shades of orange. To make 1 cup of dark orange​ paint, he needs 7 ounces of red paint and 1 ounce of yellow paint. To make 2 cups of light orange​ paint, he needs 13 ounces of yellow paint and 3 ounces of red paint. Answer parts a and b. a. Arnie buys a​ 32-oz can of red paint. Does he have enough red paint to make 3 cups of dark orange paint and 3 cups of light orange​ paint? Explain.

Answer 1

Answer:

Arnie has enough red paint

Step-by-step explanation:

step 1

Find out the number of ounces of red paint needed to make 3 cups of dark orange paint

Let

x -----> number of ounces of red paint

y -----> number of ounces of yellow paint

z ----> cups of dark orange

we know that

$\frac{x}{z}=\frac{7}{1}\ \frac{ounces\ red\ paint}{cups\ dark\ orange}$

so

For z=3 cups

substitute and solve for x

$\frac{x}{3}=\frac{7}{1}$

$x=21\ ounces\ of\ red\ paint$

step 2

Find out the number of ounces of red paint needed to make 3 cups of light orange paint

Let

x -----> number of ounces of red paint

y -----> number of ounces of yellow paint

z ----> cups of light orange

we know that

$\frac{x}{z}=\frac{3}{2}\ \frac{ounces\ red\ paint}{cups\ light\ orange}$

so

For z=3 cups

substitute and solve for x

$\frac{x}{3}=\frac{3}{2}$

$x=4.5\ ounces\ of\ red\ paint$

step 3

Adds the ounces of red paint

$21+4.5=25.5\ ounces\ of\ red\ paint$

$25.5\ ounces < 32\ ounces$

therefore

Arnie has enough red paint

Answer 2

Answer:

Arnie has enough red paint

Step-by-step explanation: