Question

At a local store, 2 bagels and 2 cups of coffee cost $4.40. The cost of 3 bagels and 4 cups of coffee is $7.80.

Part A:

Write a system of equations to represent this situation.

Part B:

Solve the system of equations by substitution and interpret its meaning.

Answer 1

Part A: Let b be the price of a bagel and c be the price of a cup of coffee.

2b + 2c = 4.40

3b + 4c = 7.80

Part B:

Solve the first equation for b:

2b + 2c = 4.40

b + c = 2.20

Substitute b = 2.20 - c into the second equation:

3(2.20 - c) + 4c = 7.80

6.60 - 3c + 4c = 7.80

c = 1.20

Substitute c = 1.20 into the equation b + c = 2.20:

b + 1.20 = 2.20

b = 1.00

The price of a bagel is $1.00 and the price of a cup of coffee is $1.20.