Question

Two airplanes are carrying food and medical supplies to a country in need. One airplane is carrying 63 meals and 57 medical kits. The total cost for those supplies on that airplane is $714. The other airplane is carrying 78 meals and 57 medical kits. The total cost for the supplies on that airplane is $789. Write and algebraically solve a system of linear equations to find the price of one meal.

Answer 1

63m + 57k = 714 ____________ (1)

78m + 57k = 789 ____________(2)

The price of one meal is $5

Explanation:

Let the price of one meal be m.

Let the price of one medical kit be k.

One airplane is carrying 63 meals and 57 medical kits and the total cost for those supplies on that airplane is $714.

This means that:

63m + 57k = 714 ____________ (1)

The other airplane is carrying 78 meals and 57 medical kits and the total cost for the supplies on that airplane is $789.

This means that:

78m + 57k = 789 ____________(2)

We now a system containing two linear equations that can be used to solve to problem:

63m + 57k = 714 ____________ (1)

78m + 57k = 789 ____________(2)

To find the price of one meal, we subtract equation (1) from (2) and simplify:

78m + 57k = 789

- 63m + 57k = 714 _

15m = 75

=> m = 75 / 15 = $5

The price of one meal is $5