SAT Math Multiple Choice Question 526: Answer and Explanation
1. A railway company normally charges $35 round trip from the suburbs of a city into downtown. The company also offers a deal for commuters who use the train frequently to commute from their homes in the suburbs to their jobs in the city. Commuters can purchase a discount card for $900, after which they only have to pay $12.50 per round trip. How many round trips, t, must a commuter make in order for the discount card to be a better deal?
- A. t < 40
- B. t > 40
- C. t < 72
- D. t > 72
Correct Answer: B
Category: Heart of Algebra / Inequalities
Strategic Advice: Translate from English into math to help you create an inequality. Then solve your inequality.
Getting to the Answer: The question states that t represents the number of round trips. The cost of one round trip without the discount card is $35 per trip, or 35t. If a commuter purchases the discount card, round trips would equal the cost of the card plus $12.50 per trip, or 900 + 12.5t. Combine these into an inequality, remembering which way the inequality symbol should be oriented. You want the cost with the discount card to be less than (<) the cost without the card, so the inequality is 900 + 12.5t < 35t. Now, solve for t:
Turn the inequality around to find that t > 40, which means a commuter must make more than 40 trips for the discount card to be a better deal, which is (B).