What you’ll learn
Create and solve equations from word problems.
Key idea
Define a variable with units, translate each phrase into an operation, and set the expressions equal to the stated total. Solve the equation and substitute the result back into the story.
A fixed fee plus a charge for each ride can be represented as fixed fee + rate × number of rides. Keep the unknown in the same role throughout the setup. The final answer should include units and satisfy any restrictions, such as a nonnegative whole-number count.
Worked example
Enter the exact value or ordered values in the format requested below.
Buying 2 equal-price items at x dollars each plus one $8 order fee costs $14. Create an equation and solve for x.
- Each of 2 items has price x, while the order fee $8 occurs once: 2x+8=14.
- Subtract 8, then divide by 2: x=(14-8)/2=3 dollars; substitution verifies the stated total.
Answer: 2x+8=14
Quick Check
Choose which candidate representation satisfies the requirements of 'Create and solve equations from word problems' and justify the choice.
There are 2 items at x dollars each, one order fee $1, total $15. Compare A: 2x+1=15; B: 2(x+1)=15; C: x+1=15. Select and justify the model, then give its price solution.