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Question

The total amount of sodium in 2 hot and 3 cups of cottage cheese is 4,720 mg. The total amount of sodium in 5 hot dogs and 2 cups of cottage cheese is 6,300 mg. How much sodium is in a hot dog? How much sodium is in a cup of cottage cheese?

Answer 1

2 unknowns with 2 equations:

Let H = mg sodium in 1 Hot dog

Let C = mg sodium in 1 cup cottage cheese

eq.1: 2H + 3C = 4720

eq. 2: 5H + 2C = 6300

Solving eq.1 for H: H = (4720 - 3C)/2

Substituting this into eq.2: 5(4720 - 3C/2) + 2C = 6300

23,600/2 - 15C/2 + 2C = 6300

11,800 - 5.5C = 6300

C = 1000 mg per cup of cottage cheese

From eq.1, 2H + 3C = 4720, thus 2H + 3000 = 4720

H = 860 mg per hot dog