Extending Your Problem Solving Skills
3-6Problem Solving: Using Charts
Overview
Organize known and unknown quantities in a chart to write an equation.
Key ideas
- Label rows by quantity (e.g., parts, totals).
- Use a variable for the unknown.
- Read the equation from the total or relationship row.
Worked examples
Example 1
Problem. A jar has nickels and dimes worth $1.25 with 17 coins total. How many of each?
Solution. Let n = nickels, dimes = 17 − n. 5n + 10(17 − n) = 125 → −5n + 170 = 125 → n = 9. 9 nickels, 8 dimes.
Practice
Try each one. Click Show answer when ready.
- 1.
12 coins, all nickels and dimes, total $0.95. Find each.
- 2.
Tickets cost $6 (adult), $4 (child). 20 tickets sold for $96. Find each.
- 3.
A board 18 ft long is cut so one piece is twice the other. Find lengths.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
A train travels at 60 mph and a car at 50 mph in the same direction. How long until the train is 30 miles ahead?
- 2.
Two planes leave the same airport. One flies east at 400 mph, the other west at 350 mph. When are they 1500 miles apart?