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A lumber company combined oak wood chips that cost $3.50 per pound with pine wood chips that cost $2.70 per pound. How many pounds of each were used to make a 50-pound mixture costing $3.02 per pound?

A) Oak wood chips: 18 pounds, Pine wood chips: 32 pounds
B) Oak wood chips: 20 pounds, Pine wood chips: 30 pounds
C) Oak wood chips: 22 pounds, Pine wood chips: 28 pounds
D) Oak wood chips: 25 pounds, Pine wood chips: 25 pounds

1 Answer

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Final answer:

To solve this problem, a system of equations is set up to represent the number of pounds of oak and pine wood chips in the mixture. By solving this system, it is determined that 20 pounds of oak wood chips and 30 pounds of pine wood chips were used to make the mixture. The cost per pound of the mixture is also calculated as $3.02. The correct answer is option B .

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let x represent the number of pounds of oak wood chips and y represent the number of pounds of pine wood chips. The total weight of the mixture is 50 pounds, so we have the equation:

x + y = 50

The cost per pound of the mixture is $3.02, so we have the equation:

3.50x + 2.70y = 3.02(50)

To solve this system, we can multiply the first equation by 2.70 and subtract it from the second equation, which will eliminate y:

3.50x + 2.70y - 2.70x - 2.70y = 3.02(50) - 2.70(50)

0.80x = 50(3.02 - 2.70)

0.80x = 50(0.32)

0.80x = 16

x = 20

Substituting this value back into the first equation, we can solve for y:

20 + y = 50

y = 50 - 20

y = 30

Therefore, the lumber company used 20 pounds of oak wood chips and 30 pounds of pine wood chips to make a 50-pound mixture costing $3.02 per pound.

User Karthick M
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