SOLUTION: A collection of nickels and dimes contains 6 more dimes than nickels. The total value of the collection is $1.95. How many nickels are there in the collection?
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Question 224690: A collection of nickels and dimes contains 6 more dimes than nickels. The total value of the collection is $1.95. How many nickels are there in the collection?
You can put this solution on YOUR website! A collection of nickels and dimes contains 6 more dimes than nickels. The total value of the collection is $1.95. How many nickels are there in the collection?
Step 1. Let x be the number of nickels.
Step 2. Let 0.05x be the dollar value of nickels.
Step 3. Let y be the number of dimes.
Step 4. Let 0.10y be the dollar value of dimes.
Step 5. Then 0.05x+0.10y=1.95 be the total dollar value.
Step 6. Also, y=x+6 since there are 6 more dimes than nickels
Step 7. Our linear system of equation is given in Steps 4 and 5 shown below:
Solve: We'll use substitution. After moving 0.1*y to the right, we get: , or . Substitute that
into another equation: and simplify: So, we know that y=15. Since , x=9.
Answer: .
So x=9 and y=15. Note there are 6 more dimes than quarters. and the total dollar value is 0.05*9+0.10*15=0.45+1.50=1.95 which is a true statement.
Step 8. ANSWER: The number of nickels is 9 and the number of dimes is 15.
I hope the above steps were helpful.
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