Question

A piggy bank contains $5.60 in nickels and dimes. The number of nickels is 8 less than 3 times the dimes. How many nickels and dimes are there in the piggy bank?

Answer 1

Answer:

24 dimes

64 nickels

Step-by-step explanation:

Answer 2

The value of the coin times the number of coins all added up equals the total value of the piggy bank
so
0.05n + 0.10d = 5.60

then they have given us "number of nickels is 8 less than 3 times the dimes"
this translates to
n = 3d - 8

we plug this into our first equation and we get
0.05(3d - 8) + 0.10d = 5.60

now we solve for d
first we can distribute the 0.05
0.15d - 0.40 + 0.10d = 5.60

then we can add the 0.15d and 0.10d together
and get
0.25d - 0.40 = 5.60

then we can add 0.40 to both sides
0.25d = 6.00

then divide both sides by 0.25
d = 6.00 / 0.25 = 24
so we have 24 dimes


then to find nickels, we plug in 24 for d into
n = 3d - 8
and get
n = 3(24) - 8
n = 72 - 8
n = 64

therefore we have
64 nickels
and
24 dimes