Baxter Tree Service charges $42 per tree to trim them, and an additional $75.50 to remove the trimmings from the property. His competitor, Barron and Son, charges $37 per tree to trim them but charges $95.50 to remove trimmings. How many trees, t, must be trimmed to make the two companies cost the same amount?
Answer:
[tex]t = 4[/tex]
Step-by-step explanation:
Baxter Tree Service:
Per tree trimming charges = $42
Additional charges for removing the trimmings from the property = $75.50
Number of trees trimmed = [tex]t[/tex]
Total charges = Additional charges + cost of trimming [tex]t[/tex] trees
Total charges = $75.50 + $42[tex]t[/tex]
Barron and Son:
Per tree trimming charges = $37
Additional charges for removing the trimmings from the property = $95.50
Number of trees trimmed = [tex]t[/tex]
Total charges = Additional charges + cost of trimming [tex]t[/tex] trees
Total charges = $95.50 + $37[tex]t[/tex]
Now, the total charges need to be same and we have to find the value of [tex]t[/tex].
[tex]75.50+42t = 95.50+37t\\\Rightarrow 42t-37t=95.50-75.50\\\Rightarrow 5t=20\\\Rightarrow \bold{t =4}[/tex]
[tex]t = 4[/tex] number of trees must be trimmed.