need to find the total of stamps

Question

Joanna enjoys collecting stamps and wants to help her two little sisters get involved in the hobby. She gives 1 8 of her stamps to her sister Kim, and gives 3 7 of the remaining stamps to her other sister, Pat. If Joanna is left with 12 stamps, then how many stamps did she have originally?

Answer 1

J= original number of stamps

Kim= 1/8 J

Pat= 3/7 of remaining= 3/7 of (J- 1/8 J) = 3/7 ·(J- 1/8 J)

Joanna is left with 12

Start with adding it all up, to see what Joanna had in the beginning, which is everything she gave to her sisters, plus what she had left.

J= 1/8 J + 3/7 ·(J- 1/8 J) +12 and then solve the equation for J

J= 1/8 J + 3/7J - 3/56 J +12 multiply whole equation by 56

56 J= 7J + 24 J - 3 J + 672 put all J's on one side, and 672 on another side, and add up all J's

.

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24 J = 672

J=24

Joanna had 24 stamps.