Section 1.5: Practice & Applications
This section combines all prior review topics: linear equations, inequalities, functions, graphs, systems, factoring, and quadratics. Work through these applied problems to solidify your understanding.
Example 1: Solving a System in Real Life
A school sold 200 tickets: adult $12, student $8. Total sales $1,760. How many adult and student tickets were sold?
Let x = adult tickets, y = student tickets
Equation 1: x + y = 200
Equation 2: 12x + 8y = 1760
From eq1: y = 200 - x
Substitute: 12x + 8(200 - x) = 1760 → 12x + 1600 - 8x = 1760 → 4x = 160 → x = 40
y = 200 - 40 = 160
Solution: 40 adult tickets, 160 student tickets
Example 2: Quadratic Application
The area of a rectangle is 48 m². The length is 2 m longer than the width. Find the dimensions.
Let width = x → length = x + 2
Equation: x(x + 2) = 48 → x² + 2x - 48 = 0
Factor: (x + 8)(x - 6) = 0 → x = 6 (reject -8)
Length = 6 + 2 = 8
Solution: width = 6 m, length = 8 m
Practice Problems
- Two numbers sum to 50. One is 3 times the other. Find the numbers.
- Tickets sold: VIP $100, regular $50. 150 tickets sold, total $10,000. How many of each type?
- Solve: 3x + 2 = 11 and check the solution
- Graph y = 2x + 1 and y = -x + 4. Find intersection.
- Factor x² + 7x + 10 and solve for x