Two customers entered Kim's bakery at the same time. One of them bought 7 bagels and 5 doughnuts, and paid $7.35. The other customer bought 4 bagels and 6 doughnuts, and paid $6.40. What is the price of each bagel and each doughnut?

the price of each bagel is $0.55 and each doughnut is $0.7

Step-by-step explanation:

Let x represent the price of each bagel.

Let y represent the price of each doughnut.

One of them bought 7 bagels and 5 doughnuts, and paid $7.35. This is expressed as

7x + 5y = 7.35 - - - - - - - - - - - - - 1

The other customer bought 4 bagels and 6 doughnuts, and paid $6.40. This is expressed as

4x + 6y = 6.4 - - - - - - - - - - - - - 2

Multiplying equation 1 by 4 and equation 2 by 7, it becomes

28x + 20y = 29.4

28x + 42y = 44.8

Subtracting, it becomes

- 22y = - 15.4

y = - 15.4/ - 22

y = 0.7

Substituting y = 0.7 into equation 1, it becomes

7x + 5 × 0.7 = 7.35

7x + 3.5 = 7.35

7x = 7.35 - 3.5

7x = 3.85

x = 3.85/7

x = 0.55

a is the correct