Bryan works as a florist. The number of bouquets he makes is given by the equation [tex]$b=\frac{3}{4} h$[/tex], where [tex]$b$[/tex] is the number of bouquets and [tex]$h$[/tex] is the number of hours. How many hours would it take him to make 6 bouquets?
A. 6
B. 8
C. 12
D. 10
E. 24
Answer (1)
Substitute the given number of bouquets, b = 6 , into the equation b = 4 3 h .
Solve the equation 6 = 4 3 h for h by multiplying both sides by 3 4 .
Simplify the equation to find h = 8 .
It would take 8 hours to make 6 bouquets, so the answer is 8 .
Explanation
Understanding the problem We are given the equation b = 4 3 h , where b is the number of bouquets and h is the number of hours. We want to find the number of hours it takes to make 6 bouquets, so we need to find h when b = 6 .
Substituting the value of b Substitute b = 6 into the equation b = 4 3 h to get 6 = 4 3 h .
Solving for h To solve for h , we multiply both sides of the equation by 3 4 : 6 × 3 4 = 4 3 h × 3 4 3 6 × 4 = h 3 24 = h 8 = h So, h = 8 .
Final Answer It would take 8 hours to make 6 bouquets.
Examples
Understanding the relationship between hours worked and output is crucial in many professions. For example, if a baker knows they can bake 20 cookies per hour, they can use this relationship to determine how many hours they need to work to fulfill a large order. Similarly, a freelance writer can estimate their earnings based on their hourly rate and the time it takes to complete an article. This type of proportional reasoning helps in planning, pricing, and managing time effectively.
