Question

Two pizzas and four sandwiches cost $62.four pizzas and ten sandwiches cost $140.how much does each pizza and sandwich cost

Answer 1

By setting up a system of equations based on the given information and solving for the variables, it is determined that each pizza costs $15 and each sandwich costs $8.

Step-by-step explanation:

To solve for the cost of each pizza and sandwich, we can set up a system of equations based on the given information:

1. Two pizzas and four sandwiches cost $62. (Equation 1)
2. Four pizzas and ten sandwiches cost $140. (Equation 2)

Let p represent the price of one pizza and s represent the price of one sandwich. We can express the given information as two linear equations:

1. 2p + 4s = 62
2. 4p + 10s = 140

Now, we can multiply equation 1 by 2 to help us eliminate one of the variables when we subtract one equation from the other:

• (2p + 4s) * 2 = 62 * 2
• 4p + 8s = 124 (Equation 3)

Subtracting equation 3 from equation 2 gives us:

1. 4p + 10s - (4p + 8s) = 140 - 124
2. 2s = 16
3. s = 16 / 2
4. s = 8

Since we now know the cost of one sandwich (s), we can substitute this back into equation 1 to find the cost of one pizza:

1. 2p + 4(8) = 62
2. 2p + 32 = 62
3. 2p = 62 - 32
4. 2p = 30
5. p = 30 / 2
6. p = 15

Therefore, each pizza costs $15, and each sandwich costs $8.