Question 155513This question is from textbook intermediate algebra
: A coin bank contains nickles, dimes and quarters. There are four times as many dimes as quarters. The value of the coins is 2.30. How many dimes are in the bank.
Please show formulas in solving.
Thanks
This question is from textbook intermediate algebra
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! We clearly have too many unknowns for the equations that we can generate, but we may still be able to work the problem.
Let x=number of quarters
And let y=number of Nickels
Now we are told that the number of dimes=4x
And we are also told that:
0.25x+0.05y+0.10(4x)=2.30 simplify
0.25x+0.40x+0.05y=2.30 collect like terms
0.65x+0.05y=2.30 multiply each term by 100 (just to get rid of the decimals)
65x+5y=230 divide each term by 5
13x+y=46 and
y=46-13x--------------------------------------------EQ1
We know a couple of things about this problem:
(1) we can't have negative numbers (negative coins are out)
(2) and we can only have whole numbers (no fractions of coins)
Looking at EQ1, we see that x (number of quarters) cannot be greater than 3 otherwise, we will start having negative nickels.So lets look at the possibilities:
If x=0, y=46 and (4x)=0
This works!
number of quarters=0, number of dimes=0 and we are left with 46 nickels which equals $2.30
If x=1, y=33 and (4x)=4
This works, also!!!!!
number of quarters=1, number of nickels=33 and number of dimes=4 for a total of $2.30
If x=2, y=20 and (4x)=8
This works, too!!!
number of quarters=2, number of nickels=20 and number of dimes=8 for a total of $2.30
If x=3, y=7 and (4x)=12
Wow!!! This also works!!!
number of quarters=3, number of nickels=7 and number of dimes=12 for a total of $2.30
So, the answer is that the number of dimes in the bank can either be 0, 4, 8, or 12
Hope this helps---ptaylor
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