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Nutz-R-Us sells cashews for $6.30 per pound and Brazil nuts for $5.00 per pound. How much of each type should be used to make a 45 pound mixture that sells for $5.64 per pound?

User Krajol
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1 Answer

20 votes
20 votes

Answer:

22.15 pounds of cashews

22.85 pounds of Brazil nuts.

Step-by-step explanation:

Let's call x the number of cashews and y the number of Brazil nuts.

If the mixture should weigh 45 pounds, we can write the following equation:

x + y = 45

On the other hand, it should be sell for $5.64, so we can write the second equation:

6.3x + 5y = 5.64(45)

6.3x + 5y = 253.8

Because 6.3 is the price per pound of the cashews, 5 is the price of the Brazil nuts and 5.64 is the price per pound of the mixture of 45 pounds.

Then, we have the following system of equation:

x + y = 45

6.3x + 5y = 253.8

Solving for y in the first equation, we get:

x + y = 45

x + y - x = 45 - x

y = 45 - x

Now, substitute y = 45 - x on the second equation:

6.3x + 5(45 - x) = 253.8

6.3x + 5(45) - 5(x) = 253.8

6.3x + 225 - 5x = 253.8

Solve for x:

1.3x + 225 = 253.8

1.3x + 225 - 225 = 253.8 - 225

1.3x = 28.8

1.3x/1.3 = 28.8/1.3

x = 22.15

Finally, substitute x = 22.15 and solve for y:

y = 45 - x

y = 45 - 22.15

y = 22.85

Therefore, the answer is:

22.15 pounds of cashews

22.85 pounds of Brazil nuts.

User Suamikim
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