wvspidermonkey
02-07-2008, 02:39 PM
The Problem:
Mary has 11 more nickels ($0.05) than quarters ($0.25). How many coins does she have if the total value of these coins are $2.65?
17 18 19 20 21
Ok... My solution...
2.65 - 11(0.05) = 2.10 To get this amount requires 7 quarters and 7 nickels. Meaning, there is a total of 25 coins (7 quarters and 18 nickels). Why is the formal answer 19?
Formal Answer: Suppose she has q quarters. then she has q + 11 nickles, and the total value of her coins, in cents, is 5(q+11) + 25q = 30q + 55 = 265. The next step... 30q = 210. Thus q=7 and the number of coins she has is q + 12 = 19.
Where did the 12 come from? What happen to the 7 other nickles?
Mary has 11 more nickels ($0.05) than quarters ($0.25). How many coins does she have if the total value of these coins are $2.65?
17 18 19 20 21
Ok... My solution...
2.65 - 11(0.05) = 2.10 To get this amount requires 7 quarters and 7 nickels. Meaning, there is a total of 25 coins (7 quarters and 18 nickels). Why is the formal answer 19?
Formal Answer: Suppose she has q quarters. then she has q + 11 nickles, and the total value of her coins, in cents, is 5(q+11) + 25q = 30q + 55 = 265. The next step... 30q = 210. Thus q=7 and the number of coins she has is q + 12 = 19.
Where did the 12 come from? What happen to the 7 other nickles?