Question

Mary and Gary had some stickers in the ratio 5:3. After Mary had given 1/3 of her stickers to Gary, the new ratio of the number of Gary’s stickers to the number of Mary’s became 7:5. If Gary then had 32 more stickers than Mary, what was the total number of stickers the 2 children had?

Answer 1

The total number of stickers the 2 children had was 192 stickers.

Let x represent Mary initial stickers, y represent Gary initial stickers and z represent the total stickers.

x + y = z

• x + y - z = 0     (1)

They shared in the ratio of 5:3, hence:

x = (5/8)z

• 8x - 5z = 0      (2)

Mary gives 1/3 of her stickers to Gary to have 32 more stickers than her.

(1/3)x = (1/3)(5/8)z = (5/24)z

y + (1/3)x = (2/3)x + 32

• y - (1/3)x = 32    (3)

Solving equation 1, 2 and 3 gives:

x = 120, y = 72, z = 192

The total number of stickers the 2 children had was 192 stickers.

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