SOLUTION: In his coin collection of dimes and quarters, Quang has 168 coins. If the collection has a value of $30. how many coins are dimes? how many are quarters?

Question 120505: In his coin collection of dimes and quarters, Quang has 168 coins. If the collection has a value of $30. how many coins are dimes? how many are quarters?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let d be the number of dimes and q be the number of quarters. Since we have two variables, we need two equations. With coin problems, you develop an equation that relates to the number of coins, and a second equation that relates to the value of those coins. Fortunately, in this problem we are given both the total number of coins and their total value.

The first thing we know is that

We also know that each dime is worth 10 cents, so the value of the dimes is 10d cents. Likewise, the value of the quarters is 25q cents. These two values add up to $30 or 3000 cents, hence:

(I converted the value from dollars to cents to avoid the messiness of decimal fraction coefficients in the equation. wouldn't really be any more difficult to solve, it is just that integers are tidier)

We can re-arrange the first equation to give us an expression for d, thus:

And then substitute this expression for d into the second equation:

Now solve for q.
Distribute and collect like terms:

Add -1680 to both sides:

Divide by 15:

Now we know that we have 88 quarters. so we have 80 dimes.

Check the answer:

80 dimes = $8.00
88 quarters = $22.00
$8.00 + $22.00 = $30.00 -- Answer checks.

Hope this helps,
John
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