Help please its Algebra 1 honors

f(x)= 50+4.25x

g(x)= 40+6.25x

(5, 71.25)

Explanation:

they are asking for the number of garmets and price of those garmets where both shops charge the same amount

if you make the two shops prices into equations you will be trying to find the line intercept

to make the lines equations

they said f(x) is cleaning company 1

g(x) is cleaning company 2

and x in the number of garmets cleaned

you can see from prices that the price does not start at 0 it has a baseline price to clean

that baseline price is the +

113.75-92.50 to find the difference in price for 5 garmets

=21.25

21.25/5 to find raise in price per 1 garmet

=4.25

now we know its 4.25x+b

baseline price = b

to find b plug in the values on the chart (first row)

4.25(5)+b=71.25

21.25+b=71.25

b=50

baseline price = 50

store 1 price is= f(x)= 50+4.25x

im gonna run out of space ill do the second one short

103.75-72.5=31.25

31.25/5=6.25

71.25=6.25(5)+x

71.25-31.25=x

x= 40= base price

g(x)= 40+6.25x

find intersection

g(x) =y

f(x) = y

y=y

therefore

50+4.25x=40+6.25x

10+4.25x=6.25x

10+4.25x=6.25x

10=2x

x=5

to find y intersection put in x to equation

y= 50+4.25x

y= 50+4.25(5)

y=50+21.25

y=71.25

intersection is (5, 71.25)