Question

im really struggling with translating word problems into equations.

"Andy as 19 coins made up of quarters and half dollars, their total value i $5.25. How many quarters does he have?"
so the numbers i have to work with are 19, 25, 50 and 5.25. Im not sure how to arrange them properly

Answer 1

maybe start with the idea that:
Q = no of quarters
H = no of half dollars

ie; the actual number of coins.

so
\(19 = Q + H \qquad🐞\)


make sense?

see the second equation ?

Answer 2

Wow YEP xD

Answer 3

further hint: so if he has Q quarters in his purse, he has $(\(Q \times \frac{1}{4}\)) in there.

Answer 4

I'm... still kind of confused.. I think... I'm not sure if I have this right--
would it be:
Q + H = 19
25Q + 50H = 5.25? and then solve by elmination ?

Answer 5

@SmileyVizard

The first equation you have is correct, but the second `25Q + 50H = 5.25` is not correct

Answer 6

25Q represents the total value of just the quarters in CENTS (not dollars)

same with 50H

so you have to convert $5.25 to cents

5.25 dollars = 5.25*100 = 525 cents

Answer 7

So the second equation would be `25Q + 50H = 525`

or you can convert everything to dollars to get `0.25Q + 0.50H = 5.25`

Answer 8

so the equation as a whole would be
Q + H = 19
25Q + 50H = 525?

Answer 9

yes that is the system of equations

Answer 10

thank you so much

Answer 11

do you see how to find Q and H from here?

Answer 12

yeah i think so

Answer 13

ok great, tell me what you get

Answer 14

okay-- give me a minute to solve it

Answer 15

sure thing, take all the time you need

Answer 16

i got H = 2 and Q = 17

Answer 17

you have the correct answer

check:

Q+H = 19
17+2 = 19
19 = 19 ... works

25Q + 50H = 525
25*17 + 50*2 = 525
525 = 525 ... works


solution (Q,H) = (17,2) is confirmed
so this proves she has 17 quarters and 2 half dollars

Answer 18

yes!!! thank you so much for your help!

Answer 19

you're welcome