Respuesta :
Answer:
Cost of a fern = $4
cost of a rose bush = $3
Step-by-step explanation:
Let cost of a fern in dollars be = [tex]x[/tex]
Let cost of a rosebush in dollars be = [tex]y[/tex]
Matt purchased 8 ferns and 1 rosebush for $35
Cost of 8 ferns in dollars will be = [tex]8x[/tex]
cost of a rosebush in dollars is = [tex]y[/tex]
Total cost of 8 ferns and 1 rosebush in dollars = [tex]8x+y[/tex]
So, we have a Matt's equation as:
[tex]8x+y=35[/tex]
Trey purchased 4 ferns and 3 rosebushes for $25.
Cost of 4 ferns in dollars = [tex]4x[/tex]
Cost of 3 rosebushes in dollars = [tex]3y[/tex]
Total cost of 4 ferns and 3 rosebush in dollars = [tex]4x+3y[/tex]
So, we have a Trey's equation as:
[tex]4x+3y=25[/tex]
The system of equations is :
A) [tex]8x+y=35[/tex]
B) [tex]4x+3y=25[/tex]
Solving the system by substitution method.
Rearranging equation A, to solve for [tex]y[/tex] in terms of [tex]x[/tex]
Subtracting both sides by [tex]8x[/tex]
[tex]8x+y-8x=35-8x[/tex]
[tex]y=35-8x[/tex]
Substituting value of [tex]y[/tex] we got from A into equation B.
[tex]4x+3(35-8x)=25[/tex]
Using distribution.
[tex]4x+105-24x=25[/tex]
Simplifying.
[tex]-20x+105=25[/tex]
Subtracting both sides by 105.
[tex]-20x+105-105=25-105[/tex]
[tex]-20x=-80[/tex]
Dividing both sides by -20.
[tex]\frac{-20x}{-20}=\frac{-80}{-20}[/tex]
∴ [tex]x=4[/tex]
We can plugin [tex]x=4[/tex] in the rearranged equation A to get value of [tex]y[/tex]
[tex]y=35-8(4)[/tex]
[tex]y=35-32[/tex]
∴ [tex]y=3[/tex]
Cost of a fern = $4
Cost of a rosebush = $3
