Overview:
Another important strategy to use when solving math problems is to identify subgoals. Some problems need to be solved in steps, and then each step can be solved separately. Many large and complex problems can be solved by using that strategy.
What Is the Overall Problem?
Suppose an assembly line is set up so that 3 workers can assemble 10 radios in 20 minutes. If all the workers on the assembly line work at the same rate, how many radios can 14 workers assemble in 90 minutes? The overall problem can be broken down into a number of steps.
How Long Does It Take One Worker?
If three workers can assemble 10 radios in 20 minutes, the rate of assembly for three workers is 10/20. Therefore, the rate of assembly for one worker will be 1/3 (10/20) or 10/60. Since we don’t know how many radios 14 workers can assemble in 60 minutes, let x equal the number of radios that 14 workers can assemble in 90 minutes. Therefore, the rate of assembly for 14 workers in 90 minutes will be x/90, and for one worker will be 1/14(x/90) or x/1260.
Setting Up and Solving the Equation:
Since the rates are equal for one worker on both sides of the equation, 10/60 should equal x/1260. Therefore, 60x should equal 12600. Solving for x, divide both sides of the equation by 60, so that x=210. In other words, 14 workers can assemble 210 radios in 90 minutes.
Checking the Solution:
In order to check the solution, check to see if the rate of assembly for one worker is the same on both sides. In other words, is 10/60 equal to 210/1260? The fraction 10/60 in simplest terms is 1/6, and so is the fraction 210/1260.
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