Question

Last year you could get a hamburger, fries, and a cola at Francisco's Drive-In for $2.00. Since the price of a hamburger has increased 10%, the price of fries has increased 30%, and the price of a cola has increased 50%, the same meal now costs $2.58. If the price of a cola is now 9 cents more than that of a hamburger, what was the price of each item last year?

Answer 1

Answer:

hamburger = h = $0.22

Fries = f = $0.96

Cola = c = $0.82

Step-by-step explanation:

Let

last year's price for each item be hamburger = h

Fries = f

Cola = c

h + f + c = 2.00 (1)

The price of a hamburger has increased by 10%

New price of hamburger = 1.10h

The price of fries has increased by 30%

New price of fries = 1.30f

The price of cola has increased by 40%

New price of cola = 1.40c

The same meal now costs $2.58.

1.1h + 1.3f + 1.4c = 2.58 (2)

If the price of a cola is now 9 cents more than that of a hamburger

1.4c = 1.1h + .09

1.4c - 1.1h = .09

Multiply (1) by 1.4

h + f + c = 2.00 × 1.4

1.4h + 1.4f + 1.4c = 2.8 (3)

1.1h + 1.3f + 1.4c = 2.58 (2)

subtract the new equation:

0.3h + 0.1f = 0.22

Multiply by 10

3h + f = 2.2

Recall,

1.4c - 1.1h = .09

1.4h + 1.4f + 1.4c = 2.8 (3)

- 1.1h + 0.0f + 1.4c = .09

Subtract

2.5h + 1.4f = 2.71

multiply by 10

25h + 14f = 27.1

Recall

3h + f = 2.2

Multiply by 14

42h + 14f = 30.8

25h + 14f = 27.1

Subtract to eliminate f

17h = 3.7

Divide both sides by 17

h = 3.7 / 17

= 0.22

h = 0.22

Substitute h into

1.4c - 1.1h = .09

1.4c - 1.1(0.22) = .09

1.4c - 0.242 = .09

1.4c = .09 + 0.242

1.4c = 1.142

Divide both sides by 1.4

c = 1.142 / 1.4

= 0.82

c = 0.82

Substitute values of c and h into

h + f + c = 2.00

0.22 + f + 0.82 = 2.00

1.04 + f = 2.00

f = 2.00 - 1.04

f = 0.96

Therefore, the price of each item last year was

hamburger = h = $0.22

Fries = f = $0.96

Cola = c = $0.82