Dried Fruit Word Problem

Question

Chloe purchased some dried mango and dried kiwi to make some trail mix. The dried mango cost $2.71 per pound and the dried kiwi cost $4.77 per pound. If she spent $30.95 for 88 pounds of dried fruit, how many pounds of each fruit did she have?

Answer 1

Chloe has a classic example of a mixing problem. She is mixing together two different ingredients. Let's let M and K represent the number of pounds of Mango and Kiwi that Chloe has purchased.

Since we know that she purchased 88 pounds of dried fruit, we can write our first equation:

M + K = 88

And since mango costs $2.71 per pound, we know she spent $2.71 * M on mango. Similarly, since kiwi costs $4.77 per pound, we know that she spent $4.77 * K on kiwi. Adding these together we get her total cost, $30.95:

$2.71 * M + $4.77 * K = $30.95

At this point, with two equations involving the two unknowns, M and K, we have what's known as a 2-by-2 system of equations.

Several methods are taught for solving these, and you should learn a few methods to attack them. The method I'll outline below is known as substitution.

First, we solve the first equation for one of the unknowns. Let's choose to solve for M. We get...

M = 88 - K

Now that we have this expression for M in terms of K, we substitute it in for M in the second equation.

$2.71 * (88 - K) + $4.77 * K = $30.95

The result is an equation involving just K. I'll give you a shot at solving that. When you've found K, you can then plug it in to the equation giving M in terms of K that we found in the first step.

I hope this helps, and if you'd like for me to step you through to the finish, or if you'd like to try another example, I'll be glad to help. :)