Need Word Prob help - SM 5B IP

[kbpaulie]

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

[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.

[Arcadia]

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

[wendyroo]

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.

[zoo_keeper]

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.