Please help me with this math problem

Question

A sum of money accounting to $3.05 consists of dimes and quarters. If there are 17 total coins, how many quarters are there?

Answer 1

Nicely done, you could also do the problem by addition/ subtraction method.

.25 q + .10 d = 3.05 multiply by 100

q + d = 17. Multiply by -10

25 q + 10 d = 305

-10 q - 10d = -170. Add or subtract

you get

15 q = 135 divide by 15

q = 9

d =8

Answer 2

Let q represent the number of quarters and d represent the number of dimes. We know that the total number of coins is 17. We can write this as an equation:

q+d=17

We also know that the total amount of money is $3.05. This can be written as an equation as well:

0.25q + 0.10d = 3.05

So we now have a system of equations involving two variables, q and d. I will solve by substitution. First I solve the first equation for d:

q+d=17

q+d-q=17-q

d=17-q

Now I will substitute this value into the second equation:

0.25q + 0.10d = 3.05

0.25q + 0.10(17-q) = 3.05

0.25q + 1.70 - 0.1q = 3.05

0.15q + 1.70 = 3.05

0.15q = 1.35

q = 1.35/0.15

q = 9

This means that we have 9 quarters.