Question

Nadia sells small boxes of chocolates and large boxes of chocolates.

The total number of chocolates in 3 small boxes and 1 large box is 66

The total number of chocolates in 1 small box and 2 large boxes is 72

Work out the number of chocolates in each small box and the number of chocolates in each large box.

Answer 1

• small box: 12
• large box: 30

Explanation:

You want the numbers of chocolates in a small box and a large box given these total numbers:

• 3 small, 1 large total 66
• 1 small, 2 large total 72

Equations

If x and y represent the numbers of chocolates in a small box and a large box, respectively, these relations can be written ...

• 3x +y = 66
• x +2y = 72

Solution

Substituting for y in the second equation, we have ...

x + 2(66 -3x) = 72

-5x +132 = 72 . . . . . . simplify

60 = 5x . . . . . . . . . add 5x-72 (keeps the numbers positive)

12 = x . . . . . . . . . . divide by 5

y = 66 -3(12) = 30 . . . . . use the expression for y to find y from x

The number in a small box is 12; the number in a large box is 30.

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