# 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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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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