Question

Hudson went into a grocery store and bought 5 peaches and 7 mangos, costing a total of $16. Austin went into the same grocery store and bought 10 peaches and 4 mangos, costing a total of $14.50. Determine the price of each peach and the price of each mango.

Answer 1

peach = $0.75, mango = $1.75

Explanation:

Let p be the price of a peach and m be the price of a mango, then

5p + 7m = 16 → (1)

10p + 4m = 14.5 → (2)

Multiplying (1) by - 2 and adding to (2) will eliminate p

- 10p - 14m = - 32 → (3)

Add (2) and (3) term by term

- 10m = - 17.5 ( divide both sides by - 10 )

m = 1.75

Substitute m = 1.75 into either of the 2 equations

Using (1)

5p + 12.25 = 16 ( subtract 12.25 from both sides )

5p = 3.75 ( divide both sides by 5 )

p = 0.75

The cost of 1 peach = $0.75 and 1 mango = $1.75