Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A financial planner is reviewing an investment portfolio. The portfolio initially had a value of $24,000. It then increased by 1/8 of its value, and later decreased by 1/6 of its *new* value. What is the final value of the portfolio?
- A$22,500
- B$25,000
- C$20,000
- D$27,000
Show answer & explanationAnswer & explanation
Correct answer: A. $22,500
First, calculate the increase: $24,000 * (1/8) = $3,000. The new value is $24,000 + $3,000 = $27,000. Then, calculate the decrease from this new value: $27,000 * (1/6) = $4,500. The final value is $27,000 - $4,500 = $22,500.
Why the other options are wrong
- B. This option might result from calculating the increase but not the subsequent decrease correctly.
- C. This option might result from incorrect calculations of percentage decrease or applying the decrease to the original value.
- D. This option is the value after only the initial increase, not accounting for the subsequent decrease.
Sequential Fractional Changes
Calculating the final value of a quantity after multiple, consecutive changes expressed as fractions, where each subsequent change is based on the *current* value.
- Each change is applied to the current total, not always the original total.
- Increases are added, decreases are subtracted.
- Fractions must be converted to their numerical values for calculation.
Memory trick: First UP, then DOWN, always from the CURRENT ground!