A shipment of 18 cars, some weighting 3000lbs a piece, and the others weighing 5000 lbs each, has a total weight of 30 tons. Find the number of each kind of car.
I start of saying X+Y = 18. THen I turn that into X=18-Y. whats next??
thank you for helping if u can.
you have to define your x and y
let the number of heavy cars be x
let the number of lighter cars be y
so, ok, at
x+y = 18
x = 18-y
5000x + 3000y = 30(2000)
divide by 1000
5x + 3y = 60
sub in your first part
5(18-y) + 3y = 60
90 - 5y + 3y = 60
-2y = -30
y = 15
There were 15 of the lighter cars, and 3 of the heavier cars
check:
15(3000) + 3(5000) = 60000 pounds = 30 tons
I enjoyed the help
You're on the right track! Let's continue solving the problem step-by-step.
1. Assign variables:
Let's say X represents the number of cars weighing 3000 lbs each.
And Y represents the number of cars weighing 5000 lbs each.
2. Create equations:
From the information given, we can create two equations:
Equation 1: X + Y = 18 (since the total number of cars is 18)
Equation 2: 3000X + 5000Y = 30 (since the total weight is 30 tons)
3. Solve the first equation for X:
X + Y = 18
X = 18 - Y
4. Substitute the value of X in the second equation:
3000(18 - Y) + 5000Y = 30
5. Simplify and solve for Y:
54000 - 3000Y + 5000Y = 30000
2000Y = 24000
Y = 12
6. Find X:
X = 18 - Y
X = 18 - 12
X = 6
Therefore, there are 6 cars that weigh 3000 lbs each and 12 cars that weigh 5000 lbs each.
To solve this problem, you can use a system of equations. Let's assume there are X cars weighing 3000 lbs each, and Y cars weighing 5000 lbs each.
1. Set up the equations based on the given information:
- Equation 1: X + Y = 18 (since the total number of cars is 18)
- Equation 2: 3000*X + 5000*Y = 30 tons
2. Simplify Equation 2 by converting the weight from tons to pounds:
- 30 tons = 30 * 2000 lbs = 60000 lbs (1 ton = 2000 lbs)
- Equation 2: 3000*X + 5000*Y = 60000 lbs
3. Now substitute X from Equation 1 into Equation 2:
- Replace X in Equation 2 with (18-Y):
- 3000*(18-Y) + 5000*Y = 60000 lbs
4. Simplify and solve for Y:
- Distribute and combine like terms in Equation 2:
- 54000 - 3000Y + 5000Y = 60000 lbs
- 2000Y = 60000 - 54000
- 2000Y = 6000
- Y = 6000/2000
- Y = 3
5. Substitute the value of Y back into Equation 1 to find X:
- X + 3 = 18
- X = 18 - 3
- X = 15
6. So there are 15 cars weighing 3000 lbs each and 3 cars weighing 5000 lbs each in the shipment.
Therefore, the number of each kind of car is: 15 cars weighing 3000 lbs and 3 cars weighing 5000 lbs.