Question

Solve using System of Linear Equations:
A deli sells three sizes of turkey sandwiches: the small turkey sandwich contains 4 ounces of meat and sells for $3.00; the regular turkey sandwich contains 9 ounces of meat an sells for $3.50; and the large turkey sandwich contains 12 ounces of meat and sells for $4.00. A customer request a selection of each size for a reception. She and the manager agree on a combination of 40 sandwiches made from 19 pounds 6 ounces of turkey for a total cost of $137. How many of each size sandwich will be in this combination?

Answer 1

you need to set up three equations (each will have 3 different variables). One variable will be the number of small sandwiches-> let's call that one "x". One variable will be the number of regular sandwiches-> let's call it "y." And one variable will be the number of large sandwiches-> let's call that "z." Now we know that you ordered 40 sandwiches in total so you're first equation is:
x+y+z = 40 (the total number of all the sandwiches you ordered)

Answer 2

You're second equation will be for the price. You know that the price was $137 in total and you also know the prices for each individual sandwich. This is the second equation:

3x + 3.5y + 4z = 137 (you multiply the price per sandwich times the number of sandwiches (your variables) for each particular size to get the total price of all the sandwiches)

Answer 3

You're third equation will be based off the weight of the sandwiches. Now you need to do some unit conversion here because it says the total weight is 19 POUNDS and 6 ounces (but since all the other weights were in ounces we are going to convert it all to ounces)
19 pounds = 304 oz (19 x 16)
+ 6 oz = 310 oz (in total)

Your equation will be:

4x +9y + 12z = 310 (you multiply the weight of each type of sandwich by the number of that type of sandwich (the variables))

Answer 4

NOw you have your 3 equations set up:

x + y + z = 40
3x + 3.5y + 4z = 137
4x + 9y + 12z = 310

Answer 5

Thank you!