Question

story problem

Answer 1

$4.40 in dimes and quarters.
23 coins in total.
Let d = number of dimes and q = number of quarters. Knowing that dimes are worth 10c and quarters 25, we can do:
0.10d + 0.25q = 4.40
d + q = 23

Now, we can use elimination (or any of a number of methods, elimination would be simple in this case though) to solve for one of the variables.
0.10d + 0.25q = 4.40

If we multiply that by 4, then there will be one q in both equations. *4 gives us:
0.40d + q = 17.60
- d + q = 23.00 subtracting the two equations
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
-0.60d + 0 = -5.40
-0.60d = -5.40
/-0.60 /-0.60
d = 9

Since the total number of coins is 23 and there are 9 dimes, that must mean there are 23 - 9 quarters. 23 - 9 = 14.

There are 14 quarters and 9 dimes. Check to make sure that's right!

Answer 2

d + q = 23 coins
10d + 25q = 440
->10d + 10q = 230
=> 15q = 210
=> q = 210/15 = 14 quarters