you have 64 coins with all being quarters and half dollars. The total value is $21.25. how many of each coin do you have?

Question

 solve using algebra

Answer 1

Hi Brooke,

 

Let

Q = # quarters

H = # half dollars

 

From the first sentence, we have

Q + H = 64

 

From the second sentence, we have

.25Q + .5H = 21.25

 

So our system of equations is

Q + H = 64

.25Q + .5H = 21.25

 

Let's multiply the 2nd equation by -4

Q + H = 64

-Q - 2H = -85

 

Now add the two equations together.  This will eliminate the variable Q.

-H = -21

H = 21

So we have 21 half dollars.

Since Q + H = 64

Q = 64-H = 64-21 = 43

We have 43 quarters.