Practice Questions Ddde43

1. **Problem:** Emma spent $75$ buying a bicycle and $27$ repairing it. She sold it for $40\%$ more than the total spent. Compare the selling price (Quantity A) to $140$ (Quantity B). 2. **Problem:** Squares RQKV and VRST each have side length $6$. Compare the area of the shaded region (Quantity A) to $36$ (Quantity B). 3. **Problem:** Property tax in Town X is $p\%$ of assessed value. In 2009, tax on a $125,000$ home was $2,500$. Compare tax on a $160,000$ home (Quantity A) to $3,000$ (Quantity B). 4. **Problem:** Given $x + y = -1$, compare $x$ (Quantity A) to $y$ (Quantity B). 5. **Problem:** $r, s, t$ are consecutive odd integers with $r < s < t$. Compare $r + s + 1$ (Quantity A) to $s + t - 1$ (Quantity B). --- ### Step-by-step solutions: 1. 1. Total spent = $75 + 27 = 102$. 2. Selling price = $102 + 0.40 \times 102 = 102 \times 1.40 = 142.8$. 3. Compare $142.8$ (Quantity A) to $140$ (Quantity B). 4. Since $142.8 > 140$, Quantity A is greater. 2. 1. Each square has area $6 \times 6 = 36$. 2. The shaded region is part of these squares; without exact shape details, assume shaded area $\leq 72$. 3. Quantity B is $36$. 4. Without exact shaded area, relationship cannot be determined. 3. 1. Tax rate $p = \frac{2500}{125000} \times 100 = 2\%$. 2. Tax on $160,000 = 2\% \times 160,000 = 3200$. 3. Compare $3200$ (Quantity A) to $3000$ (Quantity B). 4. Quantity A is greater. 4. 1. Given $x + y = -1$. 2. Without more info, cannot determine if $x > y$, $x < y$, or $x = y$. 3. Relationship cannot be determined. 5. 1. Let $r = 2k + 1$, $s = 2k + 3$, $t = 2k + 5$ for integer $k$. 2. Quantity A: $r + s + 1 = (2k + 1) + (2k + 3) + 1 = 4k + 5$. 3. Quantity B: $s + t - 1 = (2k + 3) + (2k + 5) - 1 = 4k + 7$. 4. Compare $4k + 5$ and $4k + 7$. 5. Since $4k + 7 > 4k + 5$, Quantity B is greater. **Final answers:** 1. Quantity A is greater. 2. Relationship cannot be determined. 3. Quantity A is greater. 4. Relationship cannot be determined. 5. Quantity B is greater.