SOLUTION: Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $1

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Question 155058: Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45. How many dimes does he have?
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Let n = # of nickels and d = # of dimes

Since "Joe has a collection of nickels and dimes that is worth $5.65", this means that the first equation is

Start with the first equation


Multiply every term by 100 to move the decimal point two places to the right (effectively eliminating the decimal)

Also, since "the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45", this tells us that

Distribute


Multiply


Multiply every term by 100 to move the decimal point two places to the right to make the decimal numbers whole.


Subtract 40 from both sides


Subtract. So this is our second equation

----------------------------------------------------
So we have the system of equations:




Start with the first equation


Subtract from both sides

Notice how there's a "5n" in the second equation. So simply replace the "5n" in the second equation with

Plug in


Combine like terms.


Subtract 565 from both sides.


Combine like terms


Divide both sides by 10


Reduce


So Joe has 44 dimes.


Go back to the first equation


Plug in


Multiply


Subtract 440 from both sides


Divide both sides by 5 to isolate "n"

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Answer:

So Joe has 25 nickels and 44 dimes

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