4. A certain store stocks five different brands of ice cream and sells a pint of each for \( \$ 2.75, \$ 3.25 \), \( \$ 2.50, \$ 3.25 \), and \( \$ 3.00 \), respectively. What is the positive difference between the mode price and the median price? (A) \( \$ 0.05 \) (B) \( \$ 0.25 \) (C) \( \$ 0.30 \) (D) \( \$ 0.50 \) (E) \( \$ 0.75 \) 5. The average (arithmetic mean) of three numbers is 45 . If two of the numbers are 35 and 45 , what is the third number? (A) 30 (B) 40 (C) 45 (D) 50 (E) 55 6. If the average (arithmetic mean) of \( b \) and 2 is equal to the average of \( b, 3 \), and 4 , what is the value of \( b \) ? (A) 2 (B) 4 (C) 8 (D) 10 (E) 16

**Problem 4** We have the prices: \[ \$2.75,\quad \$3.25,\quad \$2.50,\quad \$3.25,\quad \$3.00. \] 1. Identify the mode (most frequent value). The value \(\$3.25\) appears twice, so the mode is \(\$3.25\). 2. To find the median, sort the prices in increasing order: \[ \$2.50,\quad \$2.75,\quad \$3.00,\quad \$3.25,\quad \$3.25. \] The median is the middle value, which is \(\$3.00\). 3. The positive difference is: \[ \$3.25 - \$3.00 = \$0.25. \] **Problem 5** Let the three numbers be \(35\), \(45\), and \(x\). The arithmetic mean is given by: \[ \frac{35 + 45 + x}{3} = 45. \] Multiply both sides by 3: \[ 35 + 45 + x = 135. \] Combine known values: \[ 80 + x = 135. \] Solve for \(x\): \[ x = 135 - 80 = 55. \] **Problem 6** The average of \(b\) and 2 is: \[ \frac{b+2}{2}. \] The average of \(b\), 3, and 4 is: \[ \frac{b+3+4}{3} = \frac{b+7}{3}. \] Setting the two averages equal: \[ \frac{b+2}{2} = \frac{b+7}{3}. \] Multiply both sides by 6 (the least common multiple of 2 and 3): \[ 3(b+2) = 2(b+7). \] Expand both sides: \[ 3b + 6 = 2b + 14. \] Subtract \(2b\) from both sides: \[ b + 6 = 14. \] Subtract 6 from both sides: \[ b = 8. \]