a boat weighs 1500 lbs more than its motor and 1900 lbs more than its trailer. Together the boat and motor weigh five times as much as the trailer. How much does the boat weigh?
Please explain or show how to set up the equation.
Wt. of motor = X lbs.
Wt. of boat = (X+1500) lbs.
Wt. of trailer=(X+1500)-1900=X-400lbs.
X + (X+1500) = 5(X-400),
2X + 1500 = 5X - 2000,
2X - 5X = -2000 - 1500,
-3X = -3500,
X = 1167 lbs = Wt. of motor.
X+1500 = 2667 lbs = Wt. of boat.
Wt. of motor = X lbs.
Wt. of boat = (X+1500) lbs.
Wt. of trailer=(X+1500)-1900=X-400lbs.
X + (X+1500) = 5(X-400),
2X + 1500 = 5X - 2000,
2X - 5X = -2000 - 1500,
-3X = -3500,
X = 1167 lbs = Wt. of motor.
X+1500 = 2667 lbs = Wt. of boat.
To set up the equation, let's assume the weight of the motor is "m" and the weight of the trailer is "t."
Given that the boat weighs 1500 lbs more than its motor, we can express the weight of the boat as "m + 1500."
We also know that the boat weighs 1900 lbs more than its trailer, so the weight of the boat can be expressed as "t + 1900."
Additionally, the combined weight of the boat and motor is five times the weight of the trailer. Thus, we can write the equation:
(m + 1500) + m = 5t
Now, let's solve the equation to find the weight of the boat.
First, simplify the equation:
2m + 1500 = 5t
Next, rearrange the equation:
2m = 5t - 1500
Finally, divide both sides of the equation by 2 to solve for m:
m = (5t - 1500) / 2
So, the weight of the boat is (5t - 1500) / 2.