Answer: 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
, which is equal to 
, so six is the answer.
