Bakery A has baked 108 cookies and bakes 12 more each hour. Bakery B has baked 36 cookies and bakes 24 more each hour. How many hours (h) will it be before Bakery B bakes as many cookies (c) as Bakery A?
[tex]
\begin{array}{c}
c=12 h+108 \\
c=24 h+36
\end{array}
[/tex]
[?] hours
Answer (2)
Set up equations for the number of cookies baked by each bakery: c = 12 h + 108 and c = 24 h + 36 .
Equate the two expressions: 12 h + 108 = 24 h + 36 .
Simplify and solve for h : 72 = 12 h .
Find the value of h : h = 6 . The final answer is 6
Explanation
Problem Analysis Let's analyze the problem. We have two bakeries, A and B, baking cookies. Bakery A starts with 108 cookies and bakes 12 more each hour. Bakery B starts with 36 cookies and bakes 24 more each hour. We want to find out how many hours it will take for Bakery B to have baked the same number of cookies as Bakery A.
Setting up the Equations We can represent the number of cookies baked by each bakery as a function of time (h). For Bakery A, the number of cookies (c) is given by c = 12 h + 108 . For Bakery B, the number of cookies (c) is given by c = 24 h + 36 .
Equating the Number of Cookies To find the number of hours when both bakeries have baked the same number of cookies, we set the two equations equal to each other: 12 h + 108 = 24 h + 36
Isolating the Variable Now, we solve for h. First, subtract 12 h from both sides of the equation: 108 = 12 h + 36
Further Simplification Next, subtract 36 from both sides: 108 − 36 = 12 h 72 = 12 h
Solving for h Finally, divide both sides by 12: h = 12 72 h = 6
Final Answer Therefore, it will take 6 hours for Bakery B to bake as many cookies as Bakery A.
Examples
Imagine you're planning a bake-off competition between two teams. Team A starts with 108 cookies and adds 12 each hour, while Team B begins with 36 cookies but adds 24 each hour. This problem helps determine when Team B will catch up to Team A in terms of the number of cookies baked. Understanding such scenarios is useful in project management, resource allocation, and event planning, ensuring fair comparisons and strategic decision-making.
In 6 hours, Bakery B will bake the same number of cookies as Bakery A. This is determined by setting the equations for cookies baked by each bakery equal to each other and solving for hours (h). Thus, Bakery B will catch up in 6 hours.
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