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) decline 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: $\begin{array} { l }
H ( t ) = 64 - 6 t \
R ( t ) = 17 t - 143
\end{array}$ 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)July
C)November
D)October
E)August

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) decline 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:  $\begin{array} { l } 
H ( t ) = 64 - 6 t \
R ( t ) = 17 t - 143
\end{array}$   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)July
C)November
D)October
E)August

Quizplus · Accepted Answer

To find the month when the number of rakes sold equals the number of hoes sold, set $H(t) = R(t)$ and solve for $t$:$$64 - 6t = 17t - 143$$$$64 + 143 = 17t + 6t$$$$207 = 23t$$$$t = 9$$Since $t = 7$ corresponds to July, $t = 9$ corresponds to September.

The Sales of Various Types of Lawn and Garden Tools H(t)=64−6tR(t)=17t−143\begin{array} { l } H ( t ) = 64 - 6 t \\R ( t ) = 17 t - 143\end{array}H(t)=64−6tR(t)=17t−143​

The Sales of Various Types of Lawn and Garden Tools $\begin{array} { l } H ( t ) = 64 - 6 t \\R ( t ) = 17 t - 143\end{array}$