A parking meter contains quarters and dimes worth $14.30. There are 80 coins in all. Find how many of each there are

Question

1. Is there a formula
2. Is so what is it
3. Is this basic math

Answer 1

Each quarter is worth $0.25

Each dime is worth $0.10

 

Letting q = # quarters

and d = # dimes

The money in the meter is represented by

.25q + .10d

The total coins is represented by

q + d

 

From all this we have 2 equations we can write:

 

1)  q + d = 80       there are 80 coins in all

2)  .25q + .10d = 14.30    the total money is $14.30

 

We can solve this system of equations by either

substitution or elimination.   Let's eliminate the "d"

variable by multiplying equation 1 by -.1 and adding

the equations together:

 

-.10q -.10d= -8       ...  (-.1)(q+d=80)

.25q + .10d= 14.30...  equation 2

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

.15q + 0d = 6.30    ....  equation 3

 

As you see we have zero d in the new equation.

Drop the 0d and equation 3 is

 

.15q = 6.30

divide both sides by .15

.15q/.15 = 6.30/.15

q = 42

 

There are 42 quarters.

Since there are 80 coins total, the

number of dimes = 80-42 = 38

 

Check:

.25q + .10d = 14.30

.25(42) + .10(38) = 14.30

10.50 + 3.80 = 14.30

14.30 = 14.30

The equation balances and the answer is correct.