Question

Alex has been saving quarters and dimes. He found that he had 48 coins worth $9.50. How many dimes and quarters did he have?

Answer 1

is there multiple answers?

Answer 2

no

Answer 3

represent the information using 2 linear equations

Answer 4

what 2 linear equations?

Answer 5

for example, if we had 30 coins
x+y=30

Answer 6

and then another equation for the sum of the coins

Answer 7

ok, I understand how to write the first equations, but I'm not sure about the second one for the sum of coins

Answer 8

you need to decide which variable presents which coin
then multiply each coin by the value (0.10, 0.25, ,etc.)

Answer 9

I got .25x+.10y=9.50 for the second equation. is that right?

Answer 10

that looks good, nice job
this means that x is the quarters and y is the dimes

Answer 11

then how do I solve the system of equations?

Answer 12

I don't remember any methods besides substitution

x+y=48
.25x+.10y=9.50

y=48-x

\(.25x+(.10*(48-x))=9.50\\
.25x+(4.8-0.1x)=9.50\\\)

Answer 13

thank you!

Answer 14

I think I want to try it the other way around because I get a repeating decimal this way.

x+y=48
.25x+.10y=9.50

x=48-y

.25(48-y)+.10y=9.50

12-.25y+.10y=9.50
12-.15y=9.50
-.15y=-2.50
.15y=2.50
y=16.6667

looks like you can't avoid it

Answer 15

I'm pretty sure I messed something up here

Answer 16

but somehow we're supposed to have 2/3rds of a dime
http://www.wolframalpha.com/input/?i=x%2By%3D48%3B%20.25x%2B.10y%3D9.50%20&t=crmtb01