Answer: one hamburger costs $3
One hot dog costs $2.5
Step-by-step explanation:
1) Let x represent the price of one hamburger.
Let y represent the price of one hot dog.
Tim bought 3 hamburgers and 4 hot dogs for $19. It means that
3x + 4y = 19- - - - - - - - - - - - -1
John bought 5 hamburgers and 2 hot dogs for $20. It means that
5x + 2y = 20- - - - - - - - - - - - -2
Multiplying equation 1 by 5 and equation 2 by 3, it becomes
15x + 20y = 95
15x + 6y = 60
Subtracting, it becomes
14y = 35
y = 35/14
y = 2.5
Substituting y = 2.5 into equation 1, it becomes
3x + 4 × 2.5 = 19
3x + 10 = 19
3x = 19 - 10 = 9
x = 9/3
x = 3
2) Let x represent the price for one belt.
Let y represent the price for one hat.
He bought 6 belts and 8 hats for $86. This means that
6x + 8y = 86 - - - - - - - - - - - -1
At the same price, he bought 9 belts and 8 hats for $101. This means that
9x + 8y = 101 - - - - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
- 3x = - 15
x = - 15/-3
x = 5
Substituting x = 5 into equation 1, it becomes
6 × 5 + 8y = 86
30 + 8y = 86
8y = 86 - 30
8y = 56
y = 56/8
y = 7
Each belt costs $5
Each hat costs $7
