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
