Question

A restaurant serves sandwiches and salads. They sold 7 sandwiches and 7 salads for a total of $140 for lunch. In the evening, 21 sandwiches and 77 salads were sold for a total of $700. Let w represent the cost of a sandwich and d represent the cost of a salad.

Part A
Write and equation that represents the total cost at lunch time:
Write an equation that represents the total cost in the evening:

Part B
Find the cost of each sandwich (w ) using your system of equations above:

Answer 1

Hey there,

Here is what we know based on the question given:

• sold 7 sandwiches and 7 salads for $140
• sold 21 sandwiches and 77 salads for $700

Now that we know that we can answer Part A of the question given:

• Lunch time: 7w + 7d = 140
• Evening: 21w + 77d = 700

Since we have the equations now we can solve Part B:

1. Multiply the lunch time equation by 11 to cancel out one variable: 11(7w + 7d = 140) = 77w + 77d = 1540
2. Now we use the new equation to subtract the two to solve for w: (77w + 77d = 1540) - (21w + 77d = 700) = (56w = 840) w = 15

Since we have to solve for the sandwiches we now have the cost per sandwich has to be $15.

Hope I helped,

Amna

Answer 2

A) 7w + 7d = 140

21w + 77d = 700

B) $15

Explanation:

7w + 7d = 140

w + d = 20

d = 20 - w

21w + 77d = 700

3w + 11d = 100

3w + 11(20 - w) = 100

3w + 220 - 11w = 100

120 = 8w

w = 15