Jordan K. answered • 09/01/15

Tutor

4.9
(79)
Nationally Certified Math Teacher (grades 6 through 12)

Hi Michele,

Let's begin by assigning letters to represent our unknowns:

**Q = number of quarters**

**N = number of Nickels**

Now we'll come up with a system of two equations to solve for our two unknowns:

**Equation #1: Q + N = 22**

(based on total number of coins)

**Equation #2: 0.25Q + 0.05N = 3.10**

(based on total value of coins)

Now let's get rid of one unknown by combining these two equations:

**Equation #1 - (4 x Equation #2) to get rid of Q**:

4(0.25Q + 0.05N = 3.10) ---> Q + 0.20N = 12.40

Q + N = 22

- (Q + 0.20N = 12.40)

---------------------------

0.80N = 9.60

N = 9.60 / 0.80N

**N = 12 (number of nickels)**

Now we'll plug in our value for N into Equation #1 and solve for Q:

**Q + N = 22**

Q + 12 = 22

Q = 22 -12

**Q = 10 (number of quarters)**

Finally, we can verify our answers by plugging them back into Equation #2 and see if both sides match:

**0.25Q + 0.05N = 3.10**

0.25(10) + 0.05(12) = 3.10

2.50 + 0.60 = 3.10

**3.10 = 3.10 (both sides match)**

Since both sides match, we are confident that our answers are correct.

Thanks for submitting this problem and glad to help.

God bless, Jordan.