Question

Paisley has x number of dimes and y number of nickels for a total of 18 coins. Knowing that a dime is worth ten cents and a nickel is worth five cents, she wrote the system of equations below because she had a total of $1.40. Is her system correct? If not, then why?

x + y = 18

0.1x + 0.05y = 1.40

Answer 1

What do you think?

Answer 2

Look at the first equation, it might easier to start with that one.
x= number of dimes
y= number of nickels

Let's write that in place of our equation:\[\Large\rm (number~of~dimes)+(number~of~nickels)=18(coins)\]Does this first equation match up which what our paragraph is telling us?

Answer 3

Comeon Keriiiiii >.<
Gimme some feedbaccccck.
Don't just stare at the screen :3 lol

Answer 4

haha, omg i'm sorry!

Answer 5

First equation match the information?
Or does it cause a problem?

Answer 6

i think sso

Answer 7

So the first sentence is telling us that there are 18 coins, consisting of both nickels and dimes.
Ok good it looks like that equation matches the information.
Second one is a little trickier.

We know that a dime is worth 10 cents.
But we want to write cents in terms of `dollars`.
So 10 cents written in terms of dollars looks like .10, ok?
A dime is a 10th of a dollar, or .10 of a dollar.

Answer 8

So then .10 multiplying x is 10cents times the number of dimes.
So this is telling us the `values of the dimes`

Answer 9

Let's write that into our equation and see if it makes sense,\[\Large\rm 0.10x + 0.05y = 1.40\]\[\large\rm (value~of~dimes)+ (value~of~nickels) = 1.40(total~value~of~coins)\]

Answer 10

Does this one match up with our information?

Answer 11

the world may never know

Answer 12

hehe :P

Answer 13

yeh

Answer 14

Mmmk good! So it looks like her system is correct!

Answer 15

Thank you. >///<

Answer 16

No problem

Answer 17

Because I helped so much

Answer 18

haha xD