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

Algebra ->  Equations -> SOLUTION: A boat weighs 1500 pounds more than its motor and 1900 pounds more than its trailer. Together the boat and motor weigh 5 times as much as the trailer. How much does the boat weigh?      Log On


   

Question 152988This question is from textbook Algebra-Structure and Method
: A boat weighs 1500 pounds more than its motor and 1900 pounds more than its trailer. Together the boat and motor weigh 5 times as much as the trailer. How much does the boat weigh? This question is from textbook Algebra-Structure and Method

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Remember:
Boat=B=1500%2BM, weighs 1500lbs more than its motor ---------------> eqn 1
Boat=B=1900%2BT, weighs 1900lbs more than its trailer -------------> eqn 2
B%2BM=5T, Boat & motor weighs 5times the trailer ------------------> eqn 3
First, we equate both eqn 1 & 2:
1500%2BM=1900%2BT ------> M=1900%2BT-1500
M=400%2BT -----------------------------------------> eqn 4
Substitute eqn 4 in eqn 3:
B%2B400%2BT=5T ---------> B=5T-400-T
B=4T-400 ----------------------------------------> eqn 5
Substitute eqn 5 in eqn 2:
4T-400=1900%2BT
4T-T=1900%2B400
3T=2300 --------> cross%283%29T%2Fcross%283%29=cross%282300%29766.67%2Fcross%283%29
T=766.67lbs, WEIGHT OF THE TRAILER
GO BACK eqn 5 to get the weight of the Boat:
B=%284%2A766.67%29-400=3066.68-400
B=2666.68lbs, WEIGHT OF THE BOAT -----> WHAT IS ASK IN THE PROBLEM
In doubt? Go back eqn 3 to check. But 1st we get the weight of the motor via eqn 4:
M=400%2B766.67=1166.67lbs, WEIGHT OF THE MOTOR
then via eqn 3,
B%2BM=5T
2666.68%2B1166.67=5%2A766.67
3833.35lbs=3833.35lbs
Thank you,
Jojo