lucie and suzie buy greeting cards. lucie buys 10 more cards than one third of the girls’ total. how many more cards should suzie buy so that she has 10 more cards than two thirds of the girls’ total? assume that lucie does not make any purchases after her initial purchase.

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MrRoyal MrRoyal · Answer 1 · 2022-05-02T17:11:53+02:00

Lucie must buy 5 more than half of Suzie's purchase to have 10 more cards than two thirds of the girls’ total

Represent Lucie's card with L and Suzie's card with S.

So, the total number of cards is:

Total = L + S

Lucie's number of cards can be represented as:

L = 10 + 1/3(L + S)

Multiply through by 3

3L = 30 + L + S

Subtract L from both sides

2L = 30 + S

Divide by 2

L = 15 + 0.5S

Let x represents the additional number of cards.

So, we have:

x + L = 10 + 2/3(L +S)

Substitute L = 15 + 0.5S

x + 15 + 0.5S = 10 + 2/3(15 + 0.5S + S)

Evaluate the sum

x + 15 + 0.5S = 10 + 2/3(15 + 1.5S)

Expand

x + 15 + 0.5S = 10 + 10 + S

Evaluate the sum

x + 15 + 0.5S = 20 + S

Subtract 0.5S from both sides

x + 15 = 20 + 0.5S

Subtract 15 from both sides

x = 5 + 0.5S

The above means that Lucie must buy 5 more than half of Suzie's purchase to have 10 more cards than two thirds of the girls’ total

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