Question

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 1

`t = 4`

Explanation:

Baxter Tree Service:

Per tree trimming charges = $42

Additional charges for removing the trimmings from the property = $75.50

Number of trees trimmed =
`t`

Total charges = Additional charges + cost of trimming
`t` trees

Total charges = $75.50 + $42
`t`

Barron and Son:

Per tree trimming charges = $37

Additional charges for removing the trimmings from the property = $95.50

Number of trees trimmed =
`t`

Total charges = Additional charges + cost of trimming
`t` trees

Total charges = $95.50 + $37
`t`

Now, the total charges need to be same and we have to find the value of
`t`.

`75.50+42t = 95.50+37t\\\Rightarrow 42t-37t=95.50-75.50\\\Rightarrow 5t=20\\\Rightarrow \bold{t =4}`

`t = 4` number of trees must be trimmed.