Question

A chef has one cheese that contains 45% fat and another cheese that contains 20% fat. How many grams of each cheese should she use in order to obtain

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asked 2021-05-14
A chef has one cheese that contains 45% fat and another cheese that contains 20% fat. How many grams of each cheese should she use in order to obtain 30 grams of a cheese mixture that is 30% fat?

Answers (2)

2021-05-16

Correct answer is on video

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Best answer
2021-08-04

Let x be the amount of 45% fat cheese and yy be the amount of 20% fat cheese, both in grams.
The cheese mixture is 30 grams:
\(\displaystyle{x}+{y}={30}{\left({1}\right)}\)
In terms of percentage of fat, it must be 30%:
\(\displaystyle{0.45}{x}+{0.2}{y}={0.3}{\left({30}\right)}\)
\(\displaystyle{0.45}{x}+{0.2}{y}={9}{\left({2}\right)}\)
Solve by substitution. Solve for yy using (1) to obtain (3):
\(\displaystyle{y}={30}−{x}{\left({3}\right)}\)
Substitute (3) to (2) and solve for xx:
\(\displaystyle{0.45}{x}+{0.2}{\left({30}−{x}\right)}={9}\)
\(\displaystyle{0.45}{x}+{6}−{0.2}{x}={9}\)
\(\displaystyle{0.25}{x}+{6}={9}\)
\(\displaystyle{0.25}{x}={3}\)
\(\displaystyle{x}={12}\)
Solve for yy using (3):
\(\displaystyle{y}={30}−{12}\)
\(\displaystyle{y}={18}\)
So, the chef must use 12 grams of 45% fat cheese and 18 grams of 20% fat cheese.

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