Question

Please help with attached problem!

Answer 1

Madison is making a vinaigrette for her catering service using olive oil that costs fifty cent per ounce and apple cider vinegar that costs thirty-five cents an ounce. The ideal batch of vinaigrette has 25% vinegar. If she has already combined 3 cups of vinegar and 1 cup of oil, how many cups of oil should she add? What is the total cost of her completed recipe?

Answer 2

Forget the prices for now.
Just work on the amounts.

Answer 3

She needs a mixture that is 25% vinegar and 75% olive oil.
Ok so far?

Answer 4

Good

Answer 5

She needs much more oil than vinegar.
75% (oil) is 3 times 25% (vinegar), which means that for whatever amount of vinegar she uses, she needs three times as much oil.

Answer 6

So far, she has 3 cups of vinegar with only 1 cup of oil.
Her proportions are backwards.
Since she already has 3 cups of vinegar, and she can't take it back, she needs to add oil to end up with the proper ratio of oil to vinegar.
For each cup of vinegar, she needs 3 cups of oil.
She has already 3 cups of vinegar. How much total oil is needed for 3 cups of vinegar?

Answer 7

I wrote above "for whatever amount of vinegar she uses, she needs three times as much oil."
For the 3 cups of vinegar she used, how much oil is needed?

Answer 8

to make 25% she would need 12 cups?

Answer 9

No.
Read this again ""for whatever amount of vinegar she uses, she needs three times as much oil."

Answer 10

12 cups is 4 times 3 cups.
The amount of oil is 3 times the vinegar, not 4 times the vinegar.

Answer 11

So she needs 9 cups?

Answer 12

She already used 3 cups of vinegar.
The recipe needs 3 times as much oil as vinegar.
What is 3 time 3 cups?

Answer 13

Correct.
The recipe needs 9 cups of oil.

Answer 14

How much oil does she already have in the recipe she started making?

Answer 15

1 cup so she needs 8 more

Answer 16

Correct.

Answer 17

Now she adds 8 cups of oil.
She will end up with:
3 cups vinegar
9 cups oil
Now use the prices given to find the cost.
Be careful with the cost calculations because you are given prices per ounce ( I assume that to mean fluid ounces), and you are given amounts in cups.

Answer 18

1 cup = 8 fluid ounces

Answer 19

So would I add up the cost for the 3 cups of vinegar and 1 cup of oil along with the other 8 cups of oil?

Answer 20

Yes. Basically, it's 3 cups of vinegar and 9 cups of oil.
Be careful calculating the costs because you are given the costs of 1 fluid ounce of vinegar and oil, and the amounts used are cups.
Convert all the cup measurements to fluid ounces, then multiply by the costs in $/(fluid ounce)

Answer 21

@ZekeMueller
Did you get a final answer?