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Solve the following word problem using two variables and two…

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Solve the following word problem...
Solve the following word problem using two variables and two equations.

How many pounds of hamburger worth $1.05 per pound must be mixed with 60 pounds of hamburger worth $0.90 per pound to produce hamburger worth $1.00 per pound?
Submitted: 8 years ago.Category: Math Homework
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6/26/2010
Math Tutor or Teacher: abozer,
 replied 8 years ago
abozer
Category: Math Homework
Satisfied Customers: 6,159
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Hi,

Let x be the amount of $1.05 per pound hamburger and y be the amount of $0.90 per pound hamburger,

1.05x + 0.90y = 1.00(60)
x + y = 60

Multiply the second equation by -0.90,

1.05x + 0.90y = 1.00(60)
-0.90x - 0.90y = -0.90(60)

Add the two equations side by side,

0.15x = 0.10(60)
x = 40

Now substitute x = 40 in the second equation to get y,

(40) + y = 60
y = 20

So the amount of $1.05 per pound hamburger is 40 pounds and the amount of $0.90 per pound hamburger is 20 pounds.
abozer
Category: Math Homework
Satisfied Customers: 6,159
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Math Tutor or Teacher: abozer,
 replied 8 years ago
Let x be the amount of $1.05 per pound hamburger and y be the amount of $1.00 per pound hamburger,

1.05x + 0.90(60) = 1.00y
x + 60 = y

Substitute the second equation in the first one,

1.05x + 0.90(60) = 1.00(x + 60)
1.05x + 54 = x + 60
0.05x = 6
x = 120

Now substitute x = 40 in the second equation to get y,

(120) + 60 = y
y = 180

So the amount of $1.05 per pound hamburger is 120 pounds and the total amount of $1.00 per pound hamburger is 180 pounds.
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