Scenario: Phone Plans - Calculate costs using algebraic expressions!
A phone plan costs $15 per month plus $x per GB of data used. If you use the plan for 5 months and use 3 GB of data each month, write and simplify an expression for the total cost.
Problem: Total Cost = 5 months × (Monthly fee + Data cost)
Step 1: Write the expression
Total Cost = 5 × (15 + 3x)
Step 2: Apply the distributive property
5 × (15 + 3x) = 5 × 15 + 5 × 3x = 75 + 15x
Step 3: Interpret the result
75 + 15x means: $75 fixed cost + $15x for data usage
Answer: The simplified expression is 75 + 15x dollars.
Like terms have the same variable part. You can combine them by adding or subtracting their coefficients.
3x + 5y - 2x + 7y
Like terms: 3x and -2x, 5y and 7y
Simplified: (3x - 2x) + (5y + 7y) = x + 12y
2(4a - 3) + 5
Distribute: 8a - 6 + 5
Combine constants: 8a - 1
A restaurant charges $12 per person plus $2 per drink. For a group of n people who each order d drinks, write and simplify an expression for the total cost.
Solution: Total = n × 12 + n × 2d = 12n + 2nd = n(12 + 2d)
Adult tickets cost $10 and child tickets cost $6. If you buy a adult tickets and c child tickets, write and simplify an expression for the total cost.
Solution: Total = 10a + 6c (already simplified)
Simplify: 4x + 7y - 2x + 3y - 5
Your solution:
A gym membership costs $25 per month plus a one-time fee of $50. Write and simplify an expression for the total cost after m months.
Your solution: