Dennis mowed his next door neighbors lawn for a handful of dimes and nickels 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. How many of each coins did he earn
D- dimes
N-nickels
D+N=80
10d+5n=660
N=80-d
10d+5(80-d)=660
10d+400-5d=660
5d=660-400
5d=260
260 divided by 5 is 52
52 dimes and 28 nickels
Following are the calculation of the coins:
Given:
dimes and nickels coins= 80
counted coins= 6.60
To find:
calculated coins=?
Solution:
Let
N= number of Nickeles
D= number of Dimes
\(\bold{N+D=80}\\\\\bold{N=(80-D)}\)
calculate the dimes:
\(\bold{0.05N+0.10D= 6.60}\\\\\bold{0.05(80-D)+0.10D= 6.60}\\\\\bold{4 -0.05 D+0.10D= 6.60}\\\\\bold{4 +0.05D= 6.60}\\\\\bold{0.05D= 6.60-4}\\\\\bold{0.05D= 2.60}\\\\\bold{D= \frac{2.60}{0.05}\ = 52 \ dimes}\)
Calculating the nickels:
\(\bold{n=80-d}\\\\\bold{n=80-52}\\\\\bold{n=28 \ nickels }\)
Therefore, the answer is "52 dimes and 28 nickels"
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