Jeremy saves quarters and dimes. One night he counts his coins and finds that there are 30 coins with a total value of $4.50. How many of each kind of coin does he have? Write your answer as an ordered pair [e. g., if the length and width were 1 and 2 inches respectively, your answer would be (1,2) ].

Jeremey has saved 10 Quarters and 20 Dimes.  It's time to make friends.

Step-by-step explanation:

Let D and Q stand for the numbers of Dimes(D) and Quarters(Q).  Also, use pennies instead of dollars, so that 1Q = 25 and 1D = 10.  It eliminates the hassle of decimal points.

From "30 coins with a total value of $4.50"

We can write that:

D + Q = 30

and that:

10D + 25Q = 450  [the value of dimes (10D) is added to the value of quarters (25Q )]

Rearrange the first equation to isolate one of the variables and then use that relationship in the second equation.  I'll rearrange for D:

D = 30 - Q

10D + 25Q = 450  becomes:

10(30 - Q) + 25Q = 450  

300 - 10Q + 25Q = 450

15Q = 150

Q = 10

Therefore, since D + Q = 30, we find that:

D + 10 = 30

D = 20

Check the numbers:

Does

10D + 25Q = 450  ?

10(20) + 25(10) = 450 ?

200 + 250 = 450  YES

and

Does D = 30 - Q?

20 = 30 - 10  YES