Question

I need to borrow somebody's brain for a second...just need help with the set-up...not the answer

Answer 1

Peter has 48 coins. He has three times as many 10-cent coins as 20-cent coins and the
remainder are 5-cent coins. Determine the number of each coin type if their total value
is $5.10

x = 10 cent coins, y = 20 cent coins and z = 5 cent coins

I have this, but I think it is wrong

x + y + z = 48
3y = x
x - y = z
.10x + .20y + .05z = 5.10

but my answers are not coming out right

Answer 2

I am getting confused on " remainder is 5 cent coins "

Answer 3

I'm not sure why they put that part in there, but you can get away with not using "x - y = z" (not sure how you got that equation?)

you just need 3 equations to solve for 3 variables. So you can use

x + y + z = 48
3y = x
.10x + .20y + .05z = 5.10

Answer 4

But what about the remainder being 5 cent coins.....don't need that ?

Answer 5

because..
3y + y + z = 48
4y + z = 48
4y = 48 - z
y = 12 - z/4

Answer 6

I'm not sure why they wrote that. It's awkwardly phrased and unneeded.

Answer 7

It might be better to solve 4y + z = 48 for z (to avoid getting fractions)

Answer 8

4y + z = 48
z = 48 - 4y

Answer 9

.10x + .20y + .05z = 5.10

.10x + .20y + .05(48-4y) = 5.10 ... plug in z = 48 - 4y

.10(3y) + .20y + .05(48-4y) = 5.10 ... plug in x = 3y

solve for y

Answer 10

.10(3y) + .20y + .05(48 - 4y) = 5.10
.30y + .20y + 2.40 - .20y = 5.10
.30y = 5.10 - 2.40
.30y = 2.70
y = 9

3y = x
3(9) = x
36 = x

x + y + z = 48
36 + 9 + z = 48
45 + z = 48
z = 3

that works

Answer 11

thank you soooo much. I got lost on this one

Answer 12

you're welcome

Answer 13

y = 9 is correct

however, x = 36 and z = 3 are incorrect

Answer 14

awww....I guess I should have checked it. I just saw that there was 48 coins

Answer 15

27 = x....stupid mistake...I can get it now

Answer 16

your a life-saver

Answer 17

glad to be of help