Algerbraic Word Problem?

Question

I have looked in two math help books and I still can't figure out this equation!

Terry has 3 more quarters than dimes for a total of $3.55. How many quarters does he have?

I know that the answer is 11 quarters (thanks to the back of the book) but try as I might, I can't figure out how to setup the problem. Could someone please help? And if you don't mind, please explain how you decided to set it up so I can learn from it. (Example- "I put 25-x because....and I set it equal to " " for this reason...and so on.) Thank you so much to whomever helps me, because it will cease my increasing frustration.

Answer 1

Let's use Q for quarters and D for dimes.

"3 more quarters than dimes"

So if we have D, the number of dimes, then Q=D+3

"for a total of $3.55"

A quarter is 25 cents and a dime is 10 cents, so I'm going to put $3.55 into cents, 355

so 10D +25(D+3) = 355

Since D is the "number" of dimes not the "value" of the dimes I have to multiply it by how much cents each dime is worth. Same with the quarters.

So we work it out

10D + 25(D+3) = 355
10D + 25D + 75 = 355
35D + 75 = 355

and you can do it from there, right? Simple subtraction and easy division. That'll give you the number of dimes. Then you can easily figure out the number of quarters from there.

I went with D and D+3 instead of Q and Q-3, because it's usually simpler to work with a plus sign than a minus sign.

And I put it all in cents instead of using decimals because, well, do I even have to explain that? It's always easier working without decimals, especially when you have to divide in the end. :)

I hope your frustration has ceased to increase. :)

Answer 2

let
D = number of dimes
Q = number of quarters

since a dime is worth $ 0.10 then 3 dimes is 0.30 (3*0.10), 5 dimes is 0.50, and D dimes is 0.10 D
in the same fashion the quarters on hand are worth 0.25*Q
since the total worth is $3.55 we can say that the dimes plus the quarters we have are worth $3.55 in mathematical terms like this:

0.10D + 0.25Q = 3.55
we also know that Terry has 3 Quarters more than Dimes
D + 3 = Q (we add 3 to the dimes to make them equal to the quarters)
substitute for Q from the second equation into the first to get:
0.10D + 0.25(D+3) = 3.55
0.10D + 0.25D + 0.75 = 3.55
0.35 D = 2.80
D = 8
so if he had 8 dimes then he had 11 Quarters (8+3= 11)

Answer 3

d= number of dimes and q= number of quarters.
.1d + .25q = 3.55
q= d+3
.1d + .25(d+3) = 3.55
.1d +.25d + .75 = 3.55
.35d = 2.80
d = 8
8 dimes and 11 quarters

Answer 4

D + 3 = Q

.25Q + .10d = 3.55

d = q - 3

.25q + .10(q - 3) = 3.55

.25q + .10q - .30 = 3.55

.35q - .30 = 3.55

.35q = 3.85

q = 11

Answer 5

.25q+.10d=3.55
q=d+3

.25(d+3) + .10d =3.55

d=8 q=11