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Question

Can anyone explain how does the sentence ”Each girl paid $2.40 more than her share“ means that there were only 3 girls paid $2.40 more than each share, and not 4 girls?

Pls help. Thanks!

Answer

No, I dont think it means only 3 girls paid – it’s still 4 girls paid $2.40 more. 

  •  It is stated in question that 4 girls shared the cost.
  • One of them calculated wrongly and divided that amount by 3 (so each share is $2.40 more)
  • 4 girls paid that full amount
  • Therefore the amount they paid is more than the cost of the cake by ($2.40 * 4 = $9.60)

 

If you let each correct share = U 

4U+9.60 = the full amount paid

This is also equal to (4U/3) *4

So 4U / 3 * 4 = 4U + $9.60

4U = 3U + 7..20

U = $7.20 (the correct amount for each share)

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Correct: each pay -> 1/4 of cake

Incorrect: each pay -> 1/3 of cake

Difference paid by each-> 1/3 – 1/4 = 1/12

1/12 of C -> $2.40

1/4 of C -> ($2.40 ×12) ÷ 4

              = $2.40 × 3

              = $7.20 (ans)

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This is a Quantity Each Product question .

    Quantity    Each    Product 
    R1 4 1u 4u
R2 3 1u + 2.4 3u + 7.20
       

4u = 3u + 7.20

4u – 3u = 7.20

1u = 7.20

This could happen when the first girl pay 4 x 7.2 = 28.8 first.

So she 28.8 ÷ 3 = 9.6 and collect from the other 3 girls.

So they each pay 9.6 – 7.2 = 2.4 more. 

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