The sales of various types of lawn and garden tools vary according to the season. At a certain home improvement store, the monthly sales H of garden hoes (hoes sold per month) declines from July to October whereas the monthly sales of lawn rakes R (rakes sold per month) increase during this same interval. The sales of these two items during the calendar months July-October are modeled by the equations: where t is the month (t = 7 corresponds to July). In which month does the number of rakes sold equal the number of hoes sold?
A) September
B) October
C) July
D) August
E) November

Question

The sales of various types of lawn and garden tools vary according to the season. At a certain home improvement store, the monthly sales H of garden hoes (hoes sold per month) declines from July to October whereas the monthly sales of lawn rakes R (rakes sold per month) increase during this same interval. The sales of these two items during the calendar months July-October are modeled by the equations:  where t is the month (t = 7 corresponds to July). In which month does the number of rakes sold equal the number of hoes sold?
A) September 
B) October 
C) July 
D) August 
E) November

Quizplus · Accepted Answer

To find when the number of rakes sold equals the number of hoes sold, we need to set the equations equal to each other and solve for t:
11eb11e8_19a5_c102_ad38_0529576b5b77_TB4588_01

Simplifying:
11eb11e8_19a5_c102_ad38_0529576b5b77_TB4588_02

Taking the natural logarithm of both sides and using a calculator:
11eb11e8_19a5_c102_ad38_0529576b5b77_TB4588_03

So the solution is approximately t ≈ 7.99, which corresponds to August. Therefore, the answer is choice D) August.

The Sales of Various Types of Lawn and Garden Tools