chris has $2.77 in her coin jar- all in pennies, nickels, and dimes. if she has 53 coins in all and four more nickels than dimes, find how many of each tupe of coins she has
Let number of dimes = d
Then number of nickels = 4 + d ( 4 more than number of dimes)
Let number of pennies = p
total number of coins =d + 4+ d +p = 2d + 4 + p
But 2d + 4 +p = 53
2d+ p = 49
So p = 49 - 2d (*)
value of the dimes in cents =10 x d = 10d
value of the nickels in cents =5 x (4 + d) = 20 + 5d
Total value of nickels and dimes = 20 + 5d + 10 d = 20 + 15d
Total value of all coins = 20 + 15d + p = 277
Now replace p by 49 - 2d from (*) gives
20 + 15d + 49 -2d = 277
13d = 277-69 =208
d = 208/13 = 16
So he has 16 dimes, 20 nickels (4 more than dimes) and 53- 36 = 17 pennies
(check value: 160 + 100 + 17 = 277 = $ 2.77)
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