Percentage: Level 6

Solution (A): Let Spike = 100. Jerry = 20% less than Spike = 80. Tom = 25% more than Jerry = \(1.25 \times 80 = 100\). (So currently, Tom = 100, Jerry = 80, Spike = 100). Goal: Jerry needs to equal Tom (100). Jerry needs \(100 – 80 = 20\) more. Spike must give 20 to Jerry. What percent of Spike’s income is 20? \( \frac{20}{100} = 20\% \).

Solution (C): 1. \(b = c(1 – \frac{x}{100})\). 2. \(a = b(1 + \frac{x}{100})\). 3. Substitute \(b\): \(a = c(1 – \frac{x}{100})(1 + \frac{x}{100})\). 4. \(a = c(1 – \frac{x^2}{10000})\). 5. We are given \(a = c\). 6. \(c = c(1 – \frac{x^2}{10000})\). Divide by \(c\): \(1 = 1 – \frac{x^2}{10000}\). 7. \(0 = – \frac{x^2}{10000} \implies x = 0\). If \(x=0\), there is no “more” or “less”. Usually, \(x\) implies a positive change. If \(x > 0\), this is mathematically impossible because increasing and decreasing by the same percent never returns to the original value (it always results in a lower value).

Solution (B): Selling Price (SP) = 99 for each. Item 1 (Profit 10%): \(Cost \times 1.1 = 99 \implies Cost = 90\). Item 2 (Loss 10%): \(Cost \times 0.9 = 99 \implies Cost = 110\). Total Cost = \(90 + 110 = 200\). Total Sales = \(99 + 99 = 198\). Net Result = \(198 – 200 = -2\) (Loss of $2).