Question

ion.A 4 cm bean plant grows at a rate ofcm per week. A5.5 cm flower grows at a rate of cm per week. If h isthe height of the plant in centimeters and t is thenumber of weeks, then the system of equations is:h = 2t+4h = t +5.5The solution to the system,plants will both bemeans that thecentimeters tall afterweeks.

Answer 1

ANSWER

$\begin{gathered} h=7 \\ t=6 \end{gathered}$

EXPLANATION

Given;

$\begin{gathered} h=\frac{1}{2}t+4..........1 \\ h=\frac{1}{4}t+5.5.............2 \end{gathered}$

Substitute the value of h in equation 1 and 2;

$\begin{gathered} \frac{1}{2}t+4=\frac{1}{4}t+5.5 \\ \end{gathered}$

Subtract 4 from both sides;

$\begin{gathered} \frac{1}{2}t+4-4=\frac{1}{4}t+5.5-4 \\ \frac{1}{2}t=\frac{1}{4}t+1.5 \\ \frac{1}{2}t=0.25t+1.5 \\ \end{gathered}$

Subtract 0.25t from both sides;

$\begin{gathered} \frac{1}{2}t-0.25t=0.25t+1.5-0.25t \\ 0.25t=1.5 \\ t=\frac{1.5}{0.25} \\ =6 \\ t=6 \end{gathered}$

Substitute the value of t in equation 1;

$\begin{gathered} h=\frac{1}{2}t+4 \\ =\frac{1}{2}(6)+4 \\ =3+4 \\ =7 \end{gathered}$

Therefore, the solution of the system is h=7 and t=6 means that the given plant will both be 7cm tall after 6weeks.