Respuesta :
Answer:
Exactly 12 years it will take for these trees to be the same height
Step-by-step explanation:
Slope intercept form: An equation of line is in the form of [tex]y = mx+b[/tex] where m is the slope or unit rate and b is the y-intercepts.
Let x represents the time in years and y represents the height of the tree.
Use conversion:
1 ft = 12 inches
As per the given statement:
Type A is 8 feet tall and grows at a rate of 3 inches per year.
⇒unit rate per year = 3 inches = [tex]\frac{1}{4}[/tex] ft
Then, we have;
[tex]y =\frac{1}{4}x + 8[/tex] ......[1]
Similarly for;
Type B is 7 feet tall and grows at a rate of 4 inches per year.
⇒unit rate per year = 4 inches = [tex]\frac{1}{3}[/tex] ft
then;
[tex]y =\frac{1}{3}x + 7[/tex] .....[2]
To find after how many years it will take for these trees to be the same height.
Since, trees to be the same height;
⇒equate [1] and [2], to solve for x;
[tex]\frac{1}{4}x + 8 = \frac{1}{3}x +7[/tex]
Subtract 7 from both sides we get;
[tex]\frac{1}{4}x + 8-7= \frac{1}{3}x +7-7[/tex]
Simplify:
[tex]\frac{1}{4}x + 1= \frac{1}{3}x[/tex]
Subtract [tex]\frac{1}{4}x[/tex] from both sides we get;
[tex]1= \frac{1}{3}x-\frac{1}{4}x[/tex]
Simplify:
[tex]1 = \frac{x}{12}[/tex]
Multiply both sides by 12 we get;
x = 12
Therefore, exactly it will take for these trees to be the same height is, 12 years
