Question

Today we will focus on solving word problems with systems of equations. Read the following word problem.

Today’s cafeteria specials are a turkey sandwich and a pepperoni pizza. During 1st lunch, the cafeteria sold 70 turkey sandwiches and 29 pepperoni pizzas for a total of $367. During 2nd lunch, 70 turkey sandwiches and 45 pepperoni pizzas were sold for a total of $415. How much does each item cost?

How would you solve the word problem? Why would you choose that method to solve it? What is the solution?

Write at least two sentences about how you solved this problem. You can think about a new method of solving or use methods you already have learned. Also, write at least one sentence on what the solution means for the problem.

Answer 1

The pepperoni pizzas cost $3.00 each.

The cost of the turkey sandwich is $4.00

Explanation:

Let t = the number of turkey sandwiches

Let p = the number of pepperoni pizzas.

I choose to use elimination to solve.

70t + 29 p = 367 ⇒ x (-1) ⇒ -70t - 29p = -367

70t + 45p = 415 ⇒ (+) 70t + 45p = 415

16p = 48 Divide both sides by 16

p = 3

The pepperoni pizzas cost $3.00 each.

Take either of the two original equation and substitute 3 for p and solve for t.

70t + 29p = 367

70t + 29(3) = 367

70t + 87 = 367 Subtract 87 from both sides

70t + 87 - 87 = 367 - 87

70t = 280 Divide both sides by 70

t = 4

The cost of the turkey sandwich is $4.00

Check:

70t + 29p = 367

70(4) + 29(3) = 367

280 + 87 = 367

367 = 367 checks

70t + 45p = 415

70(4) + 45(3) = 415

280 + 135 = 415

415 = 415 checks

Helping in the name of Jesus.