The meat department manager at a large food store wishes

fortdefruitI

fortdefruitI

Answered question

2021-08-12

The meat department manager at a large food store wishes to mix some hamburger with 30% fat content and some hamburger that has 10% fat content in order to obtain 100 pounds of hamburger with 25% fat content.
How much of each type of hamburger should she use?

Answer & Explanation

liannemdh

liannemdh

Skilled2021-08-13Added 106 answers

Let x be the amount of 30% fat hamburger and y be the amount of 10% fat hamburger, both in pounds. The hamburger mixture is 100 pounds: x+y=100 (1) In terms of percentage of fat, it must be 25%: 0.3x+0.1y=0.25(100) (2)
0.3x+0.1y=25 Solve by substitution. Solve for y using (1) to obtain (3): y=100x (3)
Substitute (3) to (2) and solve for x: 0.3x+0.1(100x)=25
0.3x+100.1x=25
0.2x+10=25
0.2x=15 x=75
Solve for y using (3):
y=100−75
y=25
So, the manager must use 75 pounds of 30% fat hamburger and 25 grams of 10% fat hamburger.

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