algebra prroblem?

Question

If a hamburger costs 30 cents more than a hot dog and 20 cents less than a cheeseburger, and 3 hamburgers cost 75 cents less than 2 hamburgers and 2 cheeseburgers. How much does the hamburger cost?

Answer 1

Let the price of the hamburger be x cents.
So the price of the hot-dog = x-30 cents.
So the price of the cheeseburger = x + 20 cents.

From your question, 3x + 75 = 2x + 2(x + 20)
1) 3x + 75 = 2x + 2x + 40
2) 3x + 75 = 4x + 40
3) 3x + 35 = 4x
Therefore x = 35

One hamburger, thus, costs 35 cents.
(The hot dog is redundant here.)

Answer 2

Let H = Hamburger
C = Cheeseburger
D = Hot dog

Hamburger costs 30 cents more than a hot dog therefore:
H = D + 30

Hamburger costs 20 cents less than a cheeseburger therefore:
H = C - 20

3 Hamburgers cost 75 cents less than 2 hamburgers and 2 cheeseburgers therefore:
3H = 2H + 2C - 75

Using the last equation:
3H = 2H + 2C - 75 *subtract 2H from either side*
H = 2C - 75

But we also know that:
H = C -20.
Since H = C - 20 and H = 2C - 75:
C - 20 = 2C - 75 *Subtract C from either side and add 75 to either side*
55 = C

So now we now know a cheeseburger costs 55 cents and a hamburger costs 20 cents less than a cheeseburger therefore a hamburger costs 35 cents.

For the sake of completion we can now work out a hot dog costs 5 cents (30 cents less than 35 cents = 5 cents.

Hamburger: 35 cents
Cheesburger: 55 cents
Hot dog: 5 cents

Answer 3

Assume the price of a hamburger is HB.
Assume the price of a cheeseburger is CB.
All prices are in cents.
The text gives you the following relationships:
HB = CB - 20
3HB = 2HB + 2CB - 75
Now, some simplification of the 2nd equation gives:
HB = 2CB - 75
However HB = CB - 20 (from the first equation) so:
CB - 20 = 2CB - 75
After some simplification we get:
55 = CB
So if a cheeseburger costs 55 cents, a hamburger costs 35 cents (20 cents less than a cheeseburger).

Answer 4

let the hamburgers be 'ham' , cheeseburgers be 'cheese' , and hotdogs be 'dog'

ham = dog + 30
ham = cheese + 20
thus, cheese = ham - 20

3ham = 2ham + 2cheese - 75
3ham - 2ham = 2(ham - 20) - 75
ham = 2 ham - 40 - 75
2ham - ham = 40 + 75
ham = 115

therefore, each hamburger costs 1.15$ o 115 cents

Answer 5

Forget the hot dog. It just doesn't compare.
h+20=c
3h = 2h+2c-75
c-h =20
2c-h=75

It has been a long time since hamburgers and cheeseburgers were that cheap!

Answer 6

The 1st statement is extraneous.
let h=price of hamburger & c=price of cheeseburher
h=c-20
c=h+20

3h=2h+2c-75
3h-2h-2c=-75

h-2(h+20)=-75
-h-20=-75
h=75-40=35
c=55

check
3*35=2*35+2*55-75
105=70+110-75=105

Answer 7

30 cents

Answer 8

H=D+30
H=C-20
3H=2H+2C-75
H=2C-75
equating
C-20=2C-75
C=55
H=55-20=35
D=H-30=5
so costs are
hamburger=25c
hot dog=5c
cheeseburger=55c

Answer 9

hd+30=hb
cb-20=hb
2hb+2cb-75=3hb=>2cb-hb=75
2cb-40=2hb
2cb-2hb=40-----------(2)
2cb-hb=75------------(1)
(1)-(2)
hb=35cents