Cameron went into a grocery store and bought 4 apples and 7 mangos, costing a total of $17.75. Gavin went into the same grocery store and bought 2 apples and 5 mangos, costing a total of $10.75. Determine the price of each apple and the price of each mango.

the price of each apple is $2.25 and the price of each mango is $1.25

Step-by-step explanation:

Let x represent the price of one apple.

Let y represent the price of one mango.

Cameron went into a grocery store and bought 4 apples and 7 mangos, costing a total of $17.75. This means that

4x + 7y = 17.75 - - - - - - - - - - - - 1

Gavin went into the same grocery store and bought 2 apples and 5 mangos, costing a total of $10.75. This means that

2x + 5y = 10.75 - - - - - - - - - - - - -2

Multiplying equation 1 by 1 and equation 2 by 2, it becomes

4x + 7y = 17.75

4x + 10y = 21.5

Subtracting, it becomes

- 3y = - 3.75

y = - 3.75/ - 3

y = 1.25

Substituting y = 1.25 into equation 2, it becomes

2x + 5 × 1.25 = 10.75

2x + 6.25 = 10.75

2x = 10.75 - 6.25 = 4.5

x = 4.5/2 = 2.25