How to solve the equation

Question

Brayden has a piggy bank with 250 coins, dimes and quarters, worth $39.25. How many of each type of coin are there?

x=The number of dimes

y=The number of quarters

Answer 1

So we will start with what we know.

x + y = 250

and

0.10x + 0.25y = 39.25

We will solve this equation using the substitution method, one of many that can be used for this expression. So we will solve for x in the first equation:

x = 250 - y

then substitute that value into the second equation:

0.10(250 - y) + 0.25y = 39.25

25 - 0.10y + 0.25y = 39.25

0.15y = 14.25

y = 95

now we can plug in the answer for y with the first equation:

x + (95) = 250

x = 155

Now we double check our work by plugging both the x value and y value into the second equation:

0.10(155) + 0.25(95) = 39.25

15.5 + 23.75 = 39.25

39.25 = 39.25

So our final answer is:

Dimes (x) = 155

Quarters (y) = 95