The price of a cheap backpack is $15 less than an expensive backpack. When Emily bought both, she paid $75. What is the cost of the cheap backpack?
backpack cost = b
Cheap backpack = b - 15
The total of both items equals 75:
b + b - 15 = 75
Solve for b in the equation b + b - 15 = 75
Step 1: Group the b terms on the left hand side:
(1 + 1)b = 2b
Step 2: Form modified equation
2b - 15 = + 75
Step 3: Group constants:
We need to group our constants -15 and 75. To do that, we add 15 to both sides
2b - 15 + 15 = 75 + 15
Step 4: Cancel 15 on the left side:
2b = 90
Step 5: Divide each side of the equation by 2
2b/2 = 90/2
b = 45
Cheap backpack = 45 - 15 = 30
Source
backpack cost = b
Cheap backpack = b - 15
The total of both items equals 75:
b + b - 15 = 75
Solve for b in the equation b + b - 15 = 75
Step 1: Group the b terms on the left hand side:
(1 + 1)b = 2b
Step 2: Form modified equation
2b - 15 = + 75
Step 3: Group constants:
We need to group our constants -15 and 75. To do that, we add 15 to both sides
2b - 15 + 15 = 75 + 15
Step 4: Cancel 15 on the left side:
2b = 90
Step 5: Divide each side of the equation by 2
2b/2 = 90/2
b = 45
Cheap backpack = 45 - 15 = 30
Source