SOLUTION: The problem reads as follows. I have 90 coins in my piggy bank, all of which are nickels and dimes. When I count the money in the piggy bank, I find that I have $15.10. How many

Algebra ->  Customizable Word Problem Solvers  -> Coins -> SOLUTION: The problem reads as follows. I have 90 coins in my piggy bank, all of which are nickels and dimes. When I count the money in the piggy bank, I find that I have $15.10. How many      Log On

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Question 948058: The problem reads as follows.
I have 90 coins in my piggy bank, all of which are nickels and dimes. When I count the money in the piggy bank, I find that I have $15.10. How many nickels do I have and how many dimes do I have? Be sure to show all your work.
d+n= 90 d=90
0.05n +0.10d= $15.10
0.05+0.10 (90n)= 15.10
0.05n+ 9-0.10n= 15.10
0.05n-d0.10n=6.10
-0.05n=6.10
n=122
0.05 (90d) +0.10d= 15.10
4.5-0.05d+0.10d= 15.10
0.05d=10.6
d= 212
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
system%28n%2Bd=90%2C0.05n%2B0.1d=15.10%29

system%28n%2Bd=90%2Cn%2B2d=302%29

Subtract the coin count equation from the money count (simplified) equation.
This is using the Elimination Method.
highlight_green%28d=212%29
IMPOSSIBLE.

Check: If all coins were nickels, then 15.10%2F0.05=302 coins.
If all coins were dimes, then 15.10%2F%280.10%29=151 coins.
Number of total coins given was 90.
-
If all 90 coins were nickels, 0.05%2A90=40 dollars.
If they were all dimes, then 80 dollars.
Amount of money given was $15.10.

The problem description is wrong.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
something is wrong with this problem...are you sure there is 90 coins, or $15.10
if n=122 and d=+212, then d%2Bn=+122%2B212=334 coins, and

$0.05%2A122=6.1
$0.10%2A212=21.2
so, $6.10%2B21.20=27.30 which is much more then $15.10

but, when I try with $5.10, it works

total coins :
+n%2Bd=+90........equation 1
total money: $5.10
0.05n%2B0.10d=5.10.....equation 2
from equation 1 we have: n=90-d
0.05%2890-d%29%2B0.10d=5.10.....equation 2....solve for d
4.5-0.05d%2B0.10d=5.10
0.05d=5.10-4.5
0.05d=0.6
d=0.6%2F0.05
highlight%28d=12%29
then
n=90-12
highlight%28n=78%29
check:
0.05%2A78%2B0.10%2A12=5.10
3.90%2B1.20=5.10
5.10=5.10