1. **State the problem:** We have 56 students surveyed about owning bicycles and scooters. Given: 48 have bicycles, 26 have scooters, and 5 have neither. 2. **Construct the two-way table:** Let $x$ be the number of students who have both a bicycle and a scooter. - Total students: 56 - Neither bicycle nor scooter: 5 - Bicycle only: $48 - x$ - Scooter only: $26 - x$ - Both: $x$ 3. **Use the total to find $x$:** $$ (48 - x) + (26 - x) + x + 5 = 56 $$ Simplify: $$ 48 - x + 26 - x + x + 5 = 56 $$ $$ 79 - x = 56 $$ $$ \cancel{79} - x = \cancel{56} $$ $$ -x = 56 - 79 $$ $$ -x = -23 $$ $$ x = 23 $$ 4. **Fill in the table:** - Both bicycle and scooter: 23 - Bicycle only: $48 - 23 = 25$ - Scooter only: $26 - 23 = 3$ - Neither: 5 | | Scooter | No Scooter | Total | |---------------|---------|------------|-------| | Bicycle | 23 | 25 | 48 | | No Bicycle | 3 | 5 | 8 | | Total | 26 | 30 | 56 | 5. **Answer each question:** (b) Number with both bicycle and scooter: $23$ (c) Number with only scooter: $3$ (d) Percentage with only bicycle: $$ \frac{25}{56} \times 100 = 44.64\% $$ (e) Percentage of bicycle owners who also have a scooter: $$ \frac{23}{48} \times 100 = 47.92\% $$ (f) Percentage with neither: $$ \frac{5}{56} \times 100 = 8.93\% $$ (g) Percentage of students without a scooter who also do not have a bicycle: Number without scooter: 30 Number without scooter and without bicycle: 5 $$ \frac{5}{30} \times 100 = 16.67\% $$