Question

4. 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 8 fluid ounces of vinegar to 128 fluid ounces of water. 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 of vinegar contains 1 quart. What is the total number of quarts of cleaning solution that can be made using the entire bottle of vinegar? You may consider how many cups and fluid ounces are in a quart. Part D: A spray bottle holds up to 1 cup (8 fluid ounces) of the cleaning solution. When the spray bottle is full, what fraction of the cleaning solution is vinegar?

Answer 1

Part A = 4 cups of water

Part B = 5 Fluid ounces of vinegar

Part C = 17 quarts of cleaning solution

Part D = 1/17

Explanation:

We have the following conversion rates

1 cup = 8 fluid ounces

1 gallon = 128 fluid ounces

1 gallon = 16 cups

To make cleaning solution

1 cup of vinegar + 1 gallon of water to make a cleaning solution

1 cup of vinegar + 16 cups of water = cleaning solution

The ratio of vinegar to water

8 fluid ounces of vinegar : 128 fluid ounces of water.

1 cup: 16 cups

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

1 cup of vinegar + 1 gallon of water to make a cleaning solution

1 cup of vinegar = 16 cups of water

1/4 cup of vinegar =

= 1/4 cups of vinegar × 16 cups of water/ 1 cup of vinegar

= 4 cups

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

128 fluid ounces of water = 8 fluid ounces of vinegar

80 fluid ounces of water =

Cross Multiply

= 80 fluid ounces of water × 8 fluid ounces of vinegar/ 128 fluid ounces of water

= 640/128

= 5 fluid ounces of vinegar

Part C: The bottle of vinegar contains 1 quart. What is the total number of quarts of cleaning solution that can be made using the entire bottle of vinegar? You may consider how many cups and fluid ounces are in a quart.

1 bottle of vinegar = 1 quart vinegar = 4 cups vinegar

1 cup of vinegar = 16 cups of water

4 cups of vinegar =

4 × 16 = 64 cups of vinegar

Convert 64 cups of vinegar to quart

= 1 cup = 1/4 quart

64 cups = 64 × 1/4 = 16 quarts

Hence, the number of quarts of cleaning solution that can be made with 1 quart of vinegar

= 1 quart of vinegar + 16 quarts of vinegar = 17 quarts of cleaning solution

Part D: A spray bottle holds up to 1 cup (8 fluid ounces) of the cleaning solution. When the spray bottle is full, what fraction of the cleaning solution is vinegar?

8 fluid ounces of vinegar + 128 fluid ounces of water = 136 ounces of cleaning solution

136 ounces of cleaning solution = 8 fluid ounces of vinegar

8 fluid ounces of cleaning solution =

8 × 8 /136 = 64/136

= 8/17 ounces of vinegar is contained is 8 fluid ounces of cleaning solution

The fraction of vinegar in one cup of cleaning solution

= 8/17 ounces of vinegar ÷ 8 fluid ounces

= 8/17 ÷ 8

= 8/17 × 1/8

= 1/17

Therefore, when the spray bottle is full(1 cup = 8 fluid ounces, )the fraction of vinegar in the cleaning solution = 1/17