Question

To make 1000 containers of ice cream you need: 600 gallons of milk, 275 gallons of cream, and 120 gallons of flavor. Each ingredient is contained in tanks like the ones pictured below. Note the capacity of each container. Adjustments to one ingredient must be followed by corresponding adjustments to the other ingredients. If you decrease the amount of milk by 10%, how many gallons must the cream and flavor be decreased?

Answer 1

Answer:

For the cream, 32 gallons should be reduced and 12 gallons should be decreased for flavor.

Explanation:

To prepare a total of 1000 gallons of ice cream you need 600 gallons of milk, 275 gallons of cream and 120 gallons of flavor, therefore we must calculate the percentages of each ingredient, as follows:

%milk=(600/1000)x100=60%

%cream=(275/1000)x100=27.5%

%flavor=(120/1000)x100=12%

If you reduce the amount of milk by 10% you have:

Milk quantity=600 gallons-(600x0.1)=540 gallons

To maintain the same percentages of each ingredient, you must make a rule of three to know the amount of cream and flavor that would need to be used with the 540 gallons of milk. The rule of three is as follows:

540 gallons of milk------------------60%

x gallons of cream--------------------27.5%

Clearing the x:

x gallons of cream=(540x27.5)/60=243 gallons

In the same way for flavor:

540 gallons of milk------------------60%

x gallons of flavor--------------------12%

Clearing the x:

x gallons of flavor=(540x12)/60=108 gallons

Verifying that they meet the percentages that were calculated before:

Total amount of ice cream=540+243+108=891 gallons

Calculate the percentages of each ingredient:

%milk=(540/891)x100=60.6%

%cream=(243/891)x100=27.3%

%flavor=(108/891)x100=12.1%

As can be seen, it is found that approximately the same percentages calculated above are met. Therefore, we can already calculate the amount by which the cream should be reduced and the flavor.

For the cream:

Gallons of cream=275-243=32 gallons

For the flavor:

Gallons of flavor=120-108=12 gallons