A merchant wishes to mix peanuts that sell for $2.5 per pound and cashews that sell for $8 per pound to get 100 pounds of mixed nuts that sell for $4.50 per pound. Let x equal the number of pounds of peanuts and y equal the number of pounds of cashews. If solving this by writing two equations in two variables, which of the following could be one of the equations?
A) $2.5 x + 8 y = 450$
B) $2.5 x + 8 y = 4.50$
C) $x + y = 4.5$
D) $2.5 x + 8 y = 100$

Question

Quizplus · Accepted Answer

The equation should represent the total value of the mixture, which is the sum of the values of the peanuts and cashews. We can represent this as:

$2.5x + $8y = total value of nuts

We want the total value of nuts to be $4.50 per pound, so we also know that:

total value of nuts / 100 = $4.50

Simplifying this, we get:

total value of nuts = $450

Substituting into the first equation, we get:

$2.5x + $8y = $450

So the correct equation is A, which represents the total value of the mixture. None of the other choices represent the total value, and B is incorrect because it sets the total value equal to the price per pound instead of solving for it.

A Merchant Wishes to Mix Peanuts That Sell for $2 2.5x+8y=4502.5 x + 8 y = 4502.5x+8y=450

A Merchant Wishes to Mix Peanuts That Sell for $2 $2.5 x + 8 y = 450$