Question

Melanie went into a grocery store and bought 6 peaches and 8 mangos, costing a total of $14.50. Jaya went into the same grocery store and bought 7 peaches and 4 mangos, costing a total of $14.25. Write a system of equations that could be used to determine the price of each peach and the price of each mango. Define the variables that you use to write the system.

Answer 1

Mango = 0.5, Peach = 1.75

Explanation:

Let x represent the price of mango

Let y represent the price of peach

Melanie: 8x + 6y = 14.50

Jaya: 4x + 7y = 14.25

Isolate for a variable in one of the equations (just pick a random one, you don't have to pick mine)

4x + 7y = 14.25 => x = (14.25 - 7y)/4 = 3.5625 - 7/4y

Plug into other equation

8x + 6y = 14.50

8(3.5625 - 7/4y) + 6y = 14.5

28.5 - 14y + 6y = 14.5

28.5 - 14.5 = 14y - 6y

14 = 8y

y = 1.75

4x + 7y = 14.25

4x + 7(1.75) = 14.25

4x + 12.25 = 14.25

4x = 2

x = 0.5