Question

at a college, the cost of tuition increased by 11%. let x be the former cost of tuition. use the expression x + 0.11x for the new cost of tuition. write an equivalent expression by combining like terms. what does your equivalent expression tell you about how to find the new cost of tuition? choose the correct answer below. a. 0.89x; multiply the former cost by 0.89. b. 1.11x; multiply the former cost by 1.11. c. 0.89; add 0.89% of the new cost to the former cost. d. 0.11; add 0.11% of the former cost to the new cost.

Explanation:

Step1: Analyze the tuition increase

The former cost is \( x \), and the increase is \( 11\% \) of \( x \), which is \( 0.11x \). So the new cost is \( x + 0.11x \). Combining like terms, \( x + 0.11x=(1 + 0.11)x = 1.11x \). This means we multiply the former cost \( x \) by \( 1.11 \) to get the new cost.

Step2: Evaluate each option

• Option A: \( 0.89x \) would be a decrease, not an increase. Incorrect.
• Option B: \( 1.11x \) is correct for the new cost (since \( x+0.11x = 1.11x \)), and multiplying the former cost \( x \) by \( 1.11 \) gives the new cost. Correct.
• Option C: \( 0.89 \) is related to a decrease, not the increase here. Incorrect.
• Option D: The new cost is \( x + 0.11x \), not adding a percentage of the new cost. Incorrect.

Answer:

B. 1.11x; multiply the former cost by 1.11