Help on 'a boat weighs 1500 lbs more than its motor and...'

[monimac123]

A boat weighs 1500 lbs more than its motor and 1900 lbs more than its trailer. Together the boat and moter weigh 5 times as much as the trailer. How much does the boat weigh?

 

[soroban]

Re: Help on this question

Hello, monimac123!

A boat weighs 1500lbs more than its motor and 1900lbs more than its trailer.
Together the boat and moter weigh 5 times as much as the trailer.
How much does the boat weigh?

Did you set up the equations?

"Boat weighs 1500 more than Motor": $\displaystyle \,B \:=\:M\,+\,1500\;\;\Rightarrow\;\;M \:=\:B \,-\,1500\;$ [1]

"Boat weighs 1900 more than Trailer": $\displaystyle \,B\:=\:T\,+\,1900\;\;\Rightarrow\;\;T\:=\:B\,-\,1900\;$ [2]

"Boat and Motor weighs 5 times Trailer": $\displaystyle \,B\,+\,M\:=\:5T\;$ [3]


Substitute [1] and [2] into [3]:

. . . . . . . .$\displaystyle B\,+\,M\;\;\;=\;\;\;\;5T$
. . . . . . . . . . . $\displaystyle \downarrow$ . . . . . . . . .$\displaystyle \downarrow$
. . . . $\displaystyle B\,+\,\overbrace{(B\,-\,1500)}\:=\:5\overbrace{(B\,-\,1900)}$

. . . and solve for $\displaystyle B.$