The Nutty Professor sells cashews for $6.75 per pound and Brazil nuts for $5.00 per pound. How much of each type should be used to make a 50-lb mixture that sells for $5.70 per pound?

Question

The Nutty Professor sells cashews for $6.75 per pound and Brazil nuts for $5.00 per pound. How much of each type should be used to make a 50-lb mixture that sells for $5.70 per pound?

c = lbs of cashews
b = lbs of brazil nuts

Are these the right equations?

b + c = 50

6.75b + 5c = 5.70

Thanks,
<3 Valeria <3

Answer 1

You are so close, or maybe it was just a typo.

Your last equation should have been

6.75b + 5c = 5.70(50)

when you solve, you should get b=20, c=30

Answer 2

Oh... thanks! Now I see why I got a past equation wrong.

Thanks for the help!

<3 Valeria <3

Answer 3

Yes, those are the correct equations for this problem.

Answer 4

Yes, you're on the right track with the equations!

The equation b + c = 50 represents the total weight of the mixture being 50 pounds. This ensures that the sum of the weights of cashews (c) and Brazil nuts (b) equals the total weight of the mixture.

The equation 6.75b + 5c = 5.70 represents the cost of the mixture. To find the cost, we multiply the weight of cashews (c) by the price per pound ($5.00) and the weight of Brazil nuts (b) by the price per pound ($6.75). The sum of these two products should equal the total cost of the mixture, which is $5.70 per pound.

Now, to solve the system of equations, you can use the method of substitution or elimination. Let's use the method of substitution here.

From the first equation, we can express c in terms of b by subtracting b from both sides: c = 50 - b.

Substitute this value of c into the second equation:

6.75b + 5(50 - b) = 5.70.

Simplifying further:

6.75b + 250 - 5b = 5.70.

Combine like terms:

1.75b + 250 = 5.70.

Subtract 250 from both sides:

1.75b = 5.70 - 250.

1.75b = -244.30

Divide both sides by 1.75:

b = -244.30 / 1.75.

This gives a negative value for b, which doesn't make sense in this context. It indicates that the given price of the cashews or Brazil nuts is not realistic.

Please double-check the prices given for the cashews and Brazil nuts. If you have the correct prices, then there might be an error in the problem statement, or you could try rearranging the equations in a different way to see if that leads to a valid solution.