Question

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.

Answer 1

Apples are $2.25 while mangoes are $1.25.

Explanation:

We begin by converting these into simultaneous linear equations

4a + 7m = 17.75

2a + 5m = 10.75

from equation 1, we find a by

4a = 17.75 - 7m

a = 4.44 - 1.75m

We now put the value of a in equation 2

2 (4.44 - 1.75m) + 5m = 10.75

8.88 - 3.5m + 5m = 10.75

8.88 + 1.5m = 10.75

1.5m = 10.75 - 8.88

1.5m = 1.87

m = 1.25

we now put the value of m in equation 1

4a + 7(1.25) = 17.75

4a + 8.75 = 17.75

4a = 17.75 - 8.75

4a = 9

a = 2.25

Answer 2

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

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