SOLUTION: A jar containing only dimes and quarters has a total of 56 coins. The value of all the coins in the jar is $9.50. How many quarters are in the jar? How do you solve this?

Question 847398: A jar containing only dimes and quarters has a total of 56 coins. The value of all the coins in the jar is $9.50. How many quarters are in the jar? How do you solve this?
Found 2 solutions by josmiceli, josh_jordan:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = number of dimes
Let = number of quarters
-----------------------------
(1)
(2) ( in cents )
-----------------------
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)

There are 26 quarters
check:
(1)
(1)
and
(2)
(2)
(2)
OK

Answer by josh_jordan(263) (Show Source): You can put this solution on YOUR website!
To solve this word problem, we need to first convert the problem into a couple of equations. Let's see what we know:

We know there are a total of 56 coins, comprised of only dimes and quarters. In other words

d + q = 56, where d stands for dimes and q stands for quarters.

We also know that the total value of dimes and quarters is $9.50. We also know that a dime is worth 10 cents and a quarter is worth 25 cents. In other words

.10d + .25q = 9.50

We now have the two equations we need to solve our problem. Because there are two equations with 2 unknowns, this is a linear equation, and we will set it up as follows:

d + q = 56
.10d + .25q = 9.50

Let's get rid of the decimals from our second equation, to make the equation easier to work with. To do this, we will multiply our entire second equation by 100, which will give us:

10d + 25q = 950

Now we have

d + q = 56
10d + 25q = 950

Next, we need to get rid of one of our variables, so if we multiply our first equation by -10, and then add both equations together, we will be left with only q. So, when we multiply the first equation by -10, we will have

-10d + -10q = -560
10d + 25q = 950

When we add both equations together, we will obtain

15q = 390

Dividing both sides of this equation by 15 will give us the number of quarters we have:

=

q = 26

Now we know there are 26 quarters.
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