Question

You have 29 coins (only quarters and dimes). They are worth $4.55, show work using the elimination method to find out how many quarters you have.

Answer 1

well you have 2 equations here

q + d = 29 (quarters + dimes = total coins)
.25q + .10d = 4.55 (worth * amount + worth * amount = total amount)

So you can use the elimination method from here....can you do this?

Answer 2

I'm confused on how the elimination method works. Also where did you get the 10 from?

Answer 3

.10....is the worth of the dime....and .25 is the worth of the quarter.

right? a dime is 10 cents and a quarter is 25

Answer 4

and the elimination method works by eliminating 1 variable so you may solve for the other....I'll walk you through it if you would like...

Answer 5

Yes that would be great :)

Answer 6

so you have your 2 equations

q + d = 29
.25q + .10d = 4.55


What you want to do is multiply either the top or bottom equation...by a value...that will make it equal with the value in the equation below it...doing this...will eliminate a variable....in this case

q + d = 29
.25q + .10d = 4.55

notice how if you multiply the TOP equation...by .10 you'll get

.10q + .10d = 2.9

now this with the second equation below it you have

.10q + .10d = 2.9
.25q + .10d = 4.55

Now what you want to do...is subtract these 2 equations...why? because as you can see....the value of 'd' is the same in the top equation....and the bottom equation...so subtracting them will eliminate 'd'

Answer 7

so when you do that

.10q + .10d = 2.9
-(.25q + .10d = 4.55)

you get

-.15q + 0 = -1.65
(0 because there are no more 'd' left


Now you ONLY have 1 variable....'q' that is what you are going to solve for first here

divide both sides by -.15

-.15q = -1.65
-------------
-.15 -.15

and you get 11

This is how many quarters you have

To find out how many dimes....you just look at your first ORIGINAL equation....and put 11 in for 'q'

q + d = 29
we know q = 11 so

11 + d = 29
-11 -11

d = 18

Now you know you have 11 quarters...and 18 dimes

Answer 8

Hope that's understandable! :)

Answer 9

Wow, that actually was very helpful, and easy to understand! Thanks a lot :D

Answer 10

No problem! :)