SOLUTION: A person has five times as many nickels as dimes. If the total face value of these coins is $4.90, how many of each type of coin does this person have?

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Question 228903: A person has five times as many nickels as dimes. If the total face value of these coins is $4.90, how many of each type of coin does this person have?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A person has five times as many nickels as dimes. If the total face value of these coins is $4.90, how many of each type of coin does this person have?

Step 1. Let x be the number of dimes.

Step 2. Let 0.10x be the dollar value of dimes.

Step 3. Let 5x be the number of nickels.

Step 4. Let 0.05*5x=0.25x be the dollar value of nickels and since there are 5 times as many nickels as dimes.

Step 5. Then, 0.10x+.25x=4.90 be the total dollar value.

Step 6. Solving 0.10x%2B0.25x=4.90 yields the following steps:

0.35x=4.90

Divide 0.35 to both sides of the equation

0.35x%2F0.35=4.90%2F0.35

x=14 and 5x=70

Check the dollar value using the above numbers:

0.10%2A14%2B0.05%2A70=1.40%2B3.50=4.90 which is a true statement.

Step 7. ANSWER: The number of dimes is 14 and the number of nickels is 70.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J