SOLUTION: You and your friends go out to lunch. Sandwiches cost $7 each and drinks cost $2 each. You buy a total of 10 items for lunch and spend a total of $40. Write a system of linear equa

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: You and your friends go out to lunch. Sandwiches cost $7 each and drinks cost $2 each. You buy a total of 10 items for lunch and spend a total of $40. Write a system of linear equa      Log On


   

Question 1176261: You and your friends go out to lunch. Sandwiches cost $7 each and drinks cost $2 each. You buy a total of 10 items for lunch and spend a total of $40. Write a system of linear equations that describes this situation. Find the solution.
Found 2 solutions by ewatrrr, greenestamps:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
Question states:
let x be the amount of sandwiches
 $7x + $2(10-x) = $40
        $5x = $20
         x = 4 sandwiches  and 6 drinks    10-4

  $28 + $12 = $40 checks.
Wish You the Best in your Studies.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Since they want a system of linear equations, we will use two variables.

x = number of sandwiches
y = number of drinks

7x = cost of the sandwiches at $7 each
2y = cost of the drinks at $2 each

The total number of items is 10:
x%2By+=+10

The total cost is $40:
7x%2B2y+=+40

Double the first equation and compare it to the second:

7x%2B2y+=+40
2x%2B2y+=+20

The difference is

5x+=+20
x+=+4

The number of sandwiches ordered was x=4.

Informally, that means the number of drinks was 10-4 = 6.

Formally....

4%2By+=+10
y+=+10-4+=+6