lheiannie07 wrote:Each machine at a toy factory assembles a certain kind of toy at a constant rate of one toy every 3 minutes. If 40 percent of the machines at the factory are to be replaced by new machines that assemble this kind of toy at a constant rate of one toy every 2 minutes, what will be the percent increase in the number of toys assembled in one hour by all the machines at the factory, working at their constant rates?
A. 20
B. 25
C. 30
D. 40
E. 50
Since the GCF of the two times is 6, calculate the number of toys produced every 6 minutes.
Let the number of machines = 10.
10 old machines:
Since each old machine produces 1 toy in 3 minutes, 10 old machines produce 10 toys in 3 minutes.
Thus, the number of toys produced in 6 minutes -- double the amount of time -- is 20.
When 40% of the old machines are replaced by new machines, the number of new machines = (40/100)(10) = 4.
4 new machines:
Since each new machine produces 1 toy in 2 minutes, 4 toys are produced in 2 minutes.
Thus, the number of toys produced in 6 minutes -- triple the amount of time -- is 12.
6 old machines:
Since 6 old machines produce 6 toys in 3 minutes, the number of toys produced in 6 minutes -- double the amount of time -- is 12.
Total toys produced in 6 minutes by 4 new machines and 6 old machines = 12+12 = 24.
Percent increase from 20 to 24 = (difference)/(original) * 100 = (24-20)/20 * 100 = 20%.
The correct answer is
A.
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