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

Arnie needs a total of 25.5 ounces of red paint to make 3 cups of dark orange and 3 cups of light orange paints. Since he bought a 32-ounce can of red paint, he has enough paint, with 6.5 ounces left over.

Step-by-step explanation:

To determine if Arnie has enough red paint to make 3 cups of dark orange paint and 3 cups of light orange paint, we need to calculate the total amount of red paint required for both mixtures.

For dark orange paint, Arnie needs 7 ounces of red paint per cup. Therefore, for 3 cups, he will need:

7 ounces/cup x 3 cups = 21 ounces of red paint

For light orange paint, Arnie needs 3 ounces of red paint per 2 cups. Since he is making 3 cups, which is 1.5 times the amount in the recipe, he will need:

3 ounces x 1.5 = 4.5 ounces of red paint

Adding the red paint required for both dark and light orange paints:

21 ounces (dark) + 4.5 ounces (light) = 25.5 ounces of red paint in total

Since Arnie bought a 32-ounce can of red paint, he will have:

32 ounces - 25.5 ounces = 6.5 ounces of red paint left over

Arnie does have enough red paint to make 3 cups of dark orange paint and 3 cups of light orange paint.

Answer 2

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

`(x)/(z)=(7)/(1)\ (ounces\ red\ paint)/(cups\ dark\ orange)`

so

For z=3 cups

substitute and solve for x

`(x)/(3)=(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

`(x)/(z)=(3)/(2)\ (ounces\ red\ paint)/(cups\ light\ orange)`

so

For z=3 cups

substitute and solve for x

`(x)/(3)=(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