Question

At a restaurant, four hamburgers and two orders of fries cost $27.10. Three hamburgers and four orders of fries cost $25.20. If all hamburgers cost the same price and all orders of fries cost the same price, find the cost of each.

Answer 1

Each hamburger costs $5.80 and each order of fries costs $1.95.

Step-by-step explanation:

Let's represent the cost of one hamburger as x and the cost of one order of fries as y. From the given information, we can form two equations:

1. 4x + 2y = 27.10
2. 3x + 4y = 25.20

Multiplying the first equation by 2 and the second equation by 4, we get:

1. 8x + 4y = 54.20
2. 12x + 16y = 100.80

Subtracting the first equation from the second equation, we have:

12x + 16y - (8x + 4y) = 100.80 - 54.20

Simplifying, we get:

4x + 12y = 46.60

Now, we can subtract this equation from the first equation:

(4x + 2y) - (4x + 12y) = 27.10 - 46.60

Simplifying, we get:

-10y = -19.50

Dividing both sides by -10, we find that y = 1.95. Substituting this value back into the first equation, we can solve for x:

4x + 2(1.95) = 27.10

Simplifying, we get:

4x + 3.90 = 27.10

Subtracting 3.90 from both sides, we have:

4x = 23.20

Dividing both sides by 4, we find that x = 5.80.

Therefore, each hamburger costs $5.80 and each order of fries costs $1.95.

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