Question

If a client pays $300 for a mixture of nuts consisting entirely of c pounds of cashews, b pounds of brazil nuts, and m pounds of macadamia nuts, which of the following expresses b in terms of c and m? a) b = 100 - 4/3 (c+m) b) b = 100 - 4/3 (c-m) c) b = 100 + 4/3 (c+m) d) b = 100 + 3/4 (c+m)

Answer 1

To express b in terms of c and m, we need to consider the cost of the nuts and their proportions in the mixture.

The cost of cashews is typically $4 per pound, the cost of Brazil nuts is $2 per pound, and the cost of macadamia nuts is $3 per pound. Since the client pays $300 for the mixture, we can set up an equation based on the cost:

4c + 2b + 3m = 300

Now, we need to isolate b in terms of c and m. First, let's rearrange the equation:

2b = 300 - 4c - 3m

Next, divide both sides by 2:

b = (300 - 4c - 3m)/2

Now, simplify the expression:

b = 150 - 2c - (3/2)m

So, the correct expression for b in terms of c and m is:

b = 150 - 2c - (3/2)m

None of the provided options matches this expression exactly, so the closest option is:

a) b = 100 - 4/3 (c+m)

But please note that this option is not the same as the derived expression and is not an exact match.

Explanation: