A boat weighs 1500 lb more than its motor and 1900 lb more than its trailer. Together the boat and motor weigh five times as much as the trailer. How much does the boat weigh?
To find out how much the boat weighs, let's break down the information given.
Let's denote the weight of the boat as B, the weight of the motor as M, and the weight of the trailer as T.
According to the problem:
1) "A boat weighs 1500 lb more than its motor":
This can be written as B = M + 1500.
2) "A boat weighs 1900 lb more than its trailer":
This can be written as B = T + 1900.
3) "Together, the boat and motor weigh five times as much as the trailer":
This can be written as B + M = 5T.
Now, we have three equations:
B = M + 1500 (equation 1)
B = T + 1900 (equation 2)
B + M = 5T (equation 3)
To solve this system of equations, we can substitute equation 1 and 2 into equation 3. Let's start with substituting equation 1 into equation 3:
M + 1500 + M = 5T
2M + 1500 = 5T (equation 4)
Now, let's substitute equation 2 into equation 3:
T + 1900 + M = 5T
M - 4T = -1900 (equation 5)
We now have two equations (equation 4 and equation 5) with two variables (M and T). We can solve this system of equations to find the values of M and T.
From equation 5:
M - 4T = -1900
M = 4T - 1900 (equation 6)
Substitute equation 6 into equation 4:
2M + 1500 = 5T
2(4T - 1900) + 1500 = 5T
Simplify and solve for T:
8T - 3800 + 1500 = 5T
8T - 2300 = 5T
3T = 2300
T = 2300/3
Now substitute the value of T back into equation 6 to find M:
M = 4T - 1900
M = 4(2300/3) - 1900
M = 3066.67 - 1900
M = 1166.67
Since we now know the weight of the motor (M), we can substitute it into equation 1 to find B:
B = M + 1500
B = 1166.67 + 1500
B = 2666.67
Therefore, the weight of the boat (B) is approximately 2666.67 pounds.