Extending Your Problem Solving Skills
3-7Cost, Income, and Value Problems
Overview
Value problems use: number × unit value = total value. Income vs. cost gives profit.
Key ideas
- Identify number, unit value, and total.
- Sum the values for the total equation.
- Profit = income − cost.
Worked examples
Example 1
Problem. Pens cost $2; pencils cost $0.50. 10 items cost $9. Find each.
Solution. Let p = pens, pencils = 10 − p. 2p + 0.5(10 − p) = 9 → 1.5p = 4 → p ≈ ? Solve cleanly: 2p + 5 − 0.5p = 9 → 1.5p = 4 → p = 8/3. (No whole-number solution—adjust given prices in real problems.) Demonstrates checking realistic conditions.
Practice
Try each one. Click Show answer when ready.
- 1.
8 adult ($5) and child ($3) tickets cost $32. Find numbers.
- 2.
A store sold 30 items at $2 and $5 each for $96 total. Find each.
- 3.
Income $200, cost $135. Profit?
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
A ticket costs $12 for adults and $7 for children. 200 tickets were sold for $1900. How many of each?
- 2.
A merchant blends coffee worth $8/lb with coffee worth $12/lb to make 50 lb worth $10/lb. How many pounds of each?