SOLUTION: John has $2.05 in dimes and quarters. There are 3 more dimes than quarters. Find
the number of dimes and quarters. –setup system of equations and give the
solution
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the number of dimes and quarters. –setup system of equations and give the
solution
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Question 223618: John has $2.05 in dimes and quarters. There are 3 more dimes than quarters. Find
the number of dimes and quarters. –setup system of equations and give the
solution Answer by drj(1380) (Show Source):
You can put this solution on YOUR website! John has $2.05 in dimes and quarters. There are 3 more dimes than quarters. Find
the number of dimes and quarters. –setup system of equations and give the
solution
Step 1. Let x be the number of quarters.
Step 2. Let 0.25x be the dollar value of quarters.
Step 3. Let y be the number of dimes.
Step 4. Let 0.10y be the dollar value of dimes.
Step 5. Then 0.25x+0.10y=2.05 be the total dollar value.
Step 6. Also, y=x+3 since there are 3 more dimes than quarters
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=8. Since , x=5.
Answer: .
So x=5 and y=8. The difference is 3 and the total dollar value is 0.25*5+0.10*8=2.05 which is a true statement.
Step 8. ANSWER: The number of quarters is 5 and the number of dimes is 8.
I hope the above steps were helpful.
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