Question 549970: A change machine contains nickels, dimes, and quarters. There are 75 coins in he machine, and the value of the coins is $7.25. There are 5 times as many nickels as dimes. Find the number of coins of each type in the machine.
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! The problem does not say anything about the number of quarters. So, I'll assume that the number of quarters is x = number of dimes.
Based on the information given, I came up with the following equation:
5x(0.05) + 0.10(x) + 0.25(x) = 7.25
Simplifying
5x(0.05) + 0.10x + 0.025x = 7.25
Reorder the terms for easier multiplication:
5 * 0.05x + 0.10x + 0.025x = 7.25
Multiply 5 * 0.05
0.25x + 0.10x + 0.025x = 7.25
Combine like terms: 0.25x + 0.10x = 0.35x
0.35x + 0.025x = 7.25
Combine like terms: 0.35x + 0.025x = 0.375x
0.375x = 7.25
Solving
0.375x = 7.25
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '0.375'.
x = 19.33333333
Simplifying
x = 19.33333333
If there is missing information, then write back with the correct question.
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