how many quarters are there in the change?

Question

a student makes a $9.50 purchase at the bookstore with $20 bill. the store has no bills and gives change in quarters and fifty cent pieces. there are 30 coins in all. How many quarters are there in the change?

Answer 1

x = number of quarters

y = number of half dollars



Write an equation that shows the number of coins:

x + y = 30



Write an equation that shows the amount in dollars:

25x + .50y = 10.50



(We use 10.50 because that is the amount of change he received:

20 - 9.50 = 10.50)



x + y = 30

25x + .50y = 10.50



Using elimination, we can multiply the first equation by -.25

to eliminate the x terms:



-.25(x + y = 30) =



-.25x - .25y = -7.50

.25x + .50y = 10.50

------------------------------------->Add the equations together, x cancels

-------> .25y = 3.00---------->Divide both sides by .25 now =



y = 12



The student has 12 fifty-cent pieces



To find the number of quarters, use x + y = 30 and plug in

12 for y.



x + y = 30

x + 12 = 30

x + 12 - 12 = 30 - 12

x = 18



Number of quarters is 18.





CHECK: .25x + .50y = 10.50

.25(18) + .50(12) = 10.50

4.50 + 6.00 = 10.50

10.50 = 10.50 It'works



Answer: is 18 quarters (12 fifty-cent pieces)



Hope this was helpful

Answer 2

Hopefully, this can all be done with only one variable. If quarters are x, fifty cent pieces are (30-x). The amount we are looking for is 20-9.50 or 10.50. It's easier to do this all in 'pennies', so we don't have to deal with decimals.

25x + 50(30-x) = 1050

25x + 1500 - 50x = 1050

-25x = -450

x = 18.....quarters

30 - 18 = 12.......fifty cent pieces



Proof

18(0.25) + 12(0.50) = 10.50

4.50 + 6.00 = 10.50

10.50 = 10.50

Answer 3

There are 18 quarters and

12 fifty-cent pieces



The change from is $20-$9.50 = $10.50



Let the quarters be 'x' and 50-cent piece be 'y'



then

25x + 50y = 1050 ------[1]

x+y = 30 --------[2]



multiply [2] by 25 and subtract from [1]



25x+50y =1050

25x+25y=750

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

. . . . 25y = 300

. . . . . .y = 12



x+y = 30

x+12 = 30

x= 18

Answer 4

x + y = 30

0.25x + 0.50(30 - x) = 11.50

0.25x + 15 - 0.50x = 11.50

-0.25x = 11.50 - 15

-0.25x = -3.50

x = 12 quarters

18 - 50 cent pieces

Answer 5

42 quarters. 2 to get to 10 and 40 to get to 20