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Question

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Charlie had 148 pieces of $2 and $5 notes. She spent 60% of her $5 notes to buy a bag and then her mother gave her another six $2 notes. As a result, the number of $2 notes was thrice as many as the number of $5 notes left. Find the amount of money Charlie had left.

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Answer

Answer: $308.
Solution:

Let T and F be the initial numbers of $2 and $5 notes. We have

(1) T + F = 148.

After buying the bag, the number of $5 notes she has is 0.4 F.
After her receiving another six $2 notes, the number of $5 notes she has is T + 6.
We are told that she then has thrice as many $2 notes as $5 notes.

Thus,

(2) 3 × 0.4 F = T + 6.

From (1), we have T = 148 – F. Plug this into (2) to get

3 × 0.4 F = 148 – F + 6.

Rearranging, we have 2.2 F = 154, and thus F = 70.

So T = 78.

And so the money she has at the end of the day is

0.4 F × 5 + (T + 6) × 2 = 0.4 × 70 × 5 + (78 + 6) × 2 = 140 + 168 = $308.

Hope this helps and feel free to ask for any clarifications.

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0 Replies 1 Like

Let the number of 40% leftover $5 notes be 4u,
Then originally he would had 10u of $5 notes.

Since $2 notes is 3 times of leftover $5 notes, then the number of $2 notes is 12u. (From 4u x 3)

Including the six $2 notes his mother gave, the total number of notes he had before buying the bag is 154
10u + 12u = 154
22u = 154
u = 7

Number of $5 notes left = 4u =28
Value of $5 notes = 28 x 5 = $140

Number of $2 notes left = 12u = 84
Value of $2 notes = 84 x 2 = $168

Total value = $140 + $$168 = $308 ###

0 Replies 1 Like