use systems of equations to solve.?

Question

Coin collection.........
John has 20 coins totalling $ 3.20 If he has only dimes and quarters how many of each coin coin does he have?

Answer 1

Easy stuff once you know how to set up the equations =]

Let d = number of dimes
Let q = number of quarters

.1d + .25q = 3.20 Dimes are worth 10 cents, Quarters are worth 25 cents. Therefore, the number of coins times their worth should give the total.

d + q = 20 There are 20 coins, so the number of dimes and the number of quarters added together should give you 20.

I would do elimination because there are decimals involved.
Multiply the first equation by 10, and it should give you

d + 2.5q = 32

and subtract the second equation from it,

d + 2.5 q = 32
-) d + q = 20
---------------------
1.5 q = 12
q = 8

Now plug q = 8 into one of the equations. I prefer the 2nd one just because it's the easier of the two. They both should give the same answer.

d + q = 20
d + 8 = 20
d = 12

Answer: 12 dimes, 8 quarters.

Answer 2

dimes + quarters = .20
.10*dimes + .25*quarters = 3.20

dimes = d
quarters =q

d+q=20
.10d+.25q = 3.20

would start off multiplying bottom by 100 to get rid of decimals.


d+q=20
10d+25q = 320

multiplying the top by 10 we can subtract and eliminate the dimes

10d+10q = 200
10d+25q = 320
---------------------
0d+-15q=-120
q=8

using the first equation substitute in q and solve for d
d+q = 20
d+8 = 20
d=12

Check
10*12 + 25*8=320
320=320

8 quarters and 12 dimes