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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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?

2021-05-16

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.