SOLUTION: The following problem is not from a book. Jose has 6 more dimes than quaters. If his coins total $ 1.65. How many coins of each type does he have. My solution is 3 quaters and 9 d

Question 73620: The following problem is not from a book.
Jose has 6 more dimes than quaters. If his coins total $ 1.65. How many coins of each type does he have. My solution is 3 quaters and 9 dimes. However I can not put it into an equation.

Found 2 solutions by bucky, Earlsdon:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let Q equal the unknown number of quarters he has and let D equal the unknown number of dimes.
.
Since he has 6 more dimes than quarters we can say that if we added 6 to the number of
quarters that total would be the same as the number of dimes. In equation form this is:
.

.
We also know that he has 165 cents total. If we multiply the number of quarters that he has
by 25 cents per quarter that will give us the total number of cents from quarters. In the
same way, if we multiply the number of dimes times 10 cents per dime that will give us
the number of cents from dimes. Added together the number of cents from quarters and
the number of cents from dimes must total 165. In equation form this is:
.

.
From our first equation we know that D = Q + 6. Let's substitute Q + 6 for D in the second
equation that talks about cents. When we do that the second equation becomes:
.

.
Multiply on the left side to get:
.

.
Add the two terms containing Q:
.

.
Eliminate the 60 on the left side by subtracting 60 from both sides of the equation to get:
.

.
Finally divide both sides of this equation by 35 and you get:
.

.
So now we know that we have 3 quarters, just as you said. And since we know that we have
6 more dimes than quarters we know the number of dimes is .
.
There's how you can get the answer of 3 quarters and 9 dimes.
.
Hope this helps you to understand how to get the answer by mathematics.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let D = the number of dimes ($0.10) and Q = the number of quarters ($0.25).
Jose has 6 more dimes than quarters. This can be written:
D = Q+6
The total amount of money is $1.65. This can be written:
($0.10)D+($0.25)Q = $1.65 Now substitute the first equation for D here.
($0.10)(Q+6)+($0.25)Q = $1.65 Simplify and solve for Q.
($0.10)Q + $0.60 + ($0.25)Q = $1.65 Combine like-terms.
($0.35)Q + $0.60 = $1.65 Subtract $0.60 from both sides.
($0.35)Q = $1.05 Divide both sides by ($0.35)
Q = 3 This is the number of quarters Jose has.
D = Q+6
D = 3+6 = 9 This is the number of dimes Jose has.

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