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Need Word Prob help - SM 5B IP


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Can you help me w/ this, please? (SM 5B IP, pg. 38)


Eight colleagues went out for lunch together. The lunch cost $135.50. Bill paid $4.50 less than the average amount paid by the rest. How much did Bill pay?


We took $135.50/8 to get an avg or $16.93 then subtracted off the $4.50 to get $12.43


The book suggests the answer is $13.


What do you get and how? Thanks

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Guest homespun97

Looks like they rounded the total up to $140.00 then divided by 8 which is $17.50. Subtract the $4.50 and you get $13. I think the difference would be "the average amount paid by the rest" not the exact amount.

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Everyone paid $17.50

Bill paid $13


If Bill paid the same amount, than the total would be $135.50 + $4.50 = $140

Than the average for everyone would be $140/8 = $17.50

But since Bill paid less, than Bill paid $13


7($17.50)+ $13.00 = $$135.50

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7 people paid on average $A.

Therefore together they paid 7A dollars.

The eight people paid 7A + B (what Bill paid) and that totaled 135.50.

We know B = A - 4.5

7A + (A - 4.5) = 135.50

8A - 4.5 = 135.50

8A = 140

A = 17.50

B = 17.50 - 4.5 = $13.

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You can get to the answer a few ways. One, described above, looks to see what everyone would have paid if Bill had paid $4.50 more (i.e., 135.50+4.50=140), and then divided that amount by the 8 participants (140/8=17.50) and subtracted Bill's underpayment (17.50-4.50=3.50).


I thought about it differently. I took it as everyone else paid (Bill's price + $4.50). In sort, $135.50=$Bill + 7*($Bill+$4.50) = 8*$Bill + $31.50 >>>$104=8*Bill >>> Bill paid $13.

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