18) Shanee can complete 3 puzzles in [tex][tex]$4 \frac{1}{2}$[/tex][/tex] hours. Working at the same rate, how many puzzles can she complete in 15 hours?

A. 10 puzzles
B. [tex][tex]$22 \frac{1}{2}$[/tex][/tex] puzzles
C. [tex][tex]$13 \frac{1}{2}$[/tex][/tex] puzzles
D. 5 puzzles



Answer :

To determine how many puzzles Shanee can complete in 15 hours, we start by calculating her rate of completing puzzles.

1. Determine the time taken to complete 3 puzzles:
Shanee takes [tex]\( 4 \frac{1}{2} \)[/tex] hours to complete 3 puzzles. We convert [tex]\( 4 \frac{1}{2} \)[/tex] hours into a decimal:
[tex]\[ 4 \frac{1}{2} \text{ hours} = 4.5 \text{ hours} \][/tex]

2. Calculate the rate of completing puzzles:
Her rate of completing puzzles is found by dividing the number of puzzles by the time taken:
[tex]\[ \text{Rate} = \frac{\text{Number of puzzles}}{\text{Time taken}} = \frac{3 \text{ puzzles}}{4.5 \text{ hours}} = 0.6667 \text{ puzzles per hour} \][/tex]

3. Calculate the number of puzzles completed in 15 hours:
To find the number of puzzles she can complete in 15 hours, we multiply her rate by 15 hours:
[tex]\[ \text{Number of puzzles in 15 hours} = \text{Rate} \times \text{Total time} = 0.6667 \text{ puzzles per hour} \times 15 \text{ hours} = 10 \text{ puzzles} \][/tex]

Therefore, working at the same rate, Shanee can complete 10 puzzles in 15 hours. The correct answer is:

a) 10 puzzles