High School

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The directions on a bottle of vinegar say, "mix 1 cup of vinegar with 1 gallon of water to make a cleaning solution." The ratio of vinegar to water is 1 to 16.

**PART A**
How many cups of water should be mixed with 1/4 cup of vinegar to make the cleaning solution?

**PART B**
How many fluid ounces of vinegar should be mixed with 80 fluid ounces of water to make the cleaning solution?

**PART C**
The bottle contains 1 quart of vinegar. What is the total number of quarts of cleaning solution that can be made using the entire bottle of vinegar?

**PART D**
A spray bottle holds up to 1 cup of the cleaning solution. When the spray bottle is full, what fraction of the cleaning solution is vinegar?

Answer :

A. Given a 1:16 vinegar to water ratio, 1/4 cups of water would lead to 1/4*16=4 cups of water.

B. Using the same ratio, 80/16=5 fluid ounces of vinegar.

C. Again, using the ratio, 16 quarts of water will be added. This plus the quart of vinegar is a total of 17 quarts.

D. 1:16 is the vinegar to water ratio. Thus, for every 1 unit of vinegar, there will be 1+16=17 total units. Thus, the fraction is 1/17. Note that the spray bottle does not necessarily need to be full for this solution to work.

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Rewritten by : Barada

Final answer:

To make a cleaning solution, for every 1/4 cup of vinegar, you need 4 cups of water, for every 80 fl oz of water, 5 fl oz of vinegar, 1 quart of vinegar makes 17 quarts of solution, and a full 1 cup spray bottle contains 1/16 vinegar.

Explanation:

The student's question involves calculating proportions and unit conversions within the context of mixing vinegar and water to create a cleaning solution.

PART A

Since the ratio of vinegar to water is 1:16, and the student wishes to use 1/4 cup of vinegar, the necessary calculation is:

1/4 cup vinegar * 16 cups water/cup vinegar = 4 cups water.

PART B

To find the amount of vinegar needed for 80 fl oz of water, use the ratio:

1 cup vinegar / 16 cups water = x fl oz vinegar / 80 fl oz water.

After converting cups to fluid ounces (1 cup = 8 fl oz) and performing the cross-multiplication, x equals 5 fl oz of vinegar.

PART C

Since 1 quart is equal to 4 cups, and each 1 cup of vinegar is mixed with 16 cups of water, a quart of vinegar can make 17 quarts of cleaning solution:

(1 cup vinegar + 16 cups water) * 4 = 17 quarts of solution.

PART D

For a filled 1 cup (8 fl oz) spray bottle, the proportion of vinegar, which is 1/2 fl oz, to the cleaning solution is:

1/2 fl oz vinegar / 8 fl oz solution = 1/16, so the solution is 1/16 vinegar.

Learn more about Mixing Ratios here:

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