Question

Trains Two trains, Train A and Train B, weigh a total of 262 tons. Train A is heavier than Train B. The difference of their weights is 204 tons. What is the weight of each train?
How much does rain A weight?

Answer 1

Are you sure

Answer 2

Writing Solve the system using addition. Use pencil and paper. Explain why the addition method is a good choice for solving the system. If you wanted to solve for x first, is the addition method still a good choice? Explain.
x - 2.8y = 0.6
-X + 3.9y = - 2.8
The solution is ___. (Type an ordered pair)

Answer 3

Let's denote the weight of Train A as x tons and the weight of Train B as y tons.

According to the given information, the total weight of both trains is 262 tons:
x + y = 262

We also know that Train A is heavier than Train B by 204 tons:
x - y = 204

Now we can solve these two equations simultaneously:

From the first equation: x = 262 - y
Substitute x in the second equation: 262 - y - y = 204
262 - 2y = 204
-2y = -58
y = 29

So the weight of Train B is 29 tons.

Now, we can find the weight of Train A using the first equation:
x + 29 = 262
x = 262 - 29
x = 233

Therefore, the weight of Train A is 233 tons.

Answer 4

Let's re-derive the solution for this problem:

Let the weight of Train A be x tons and the weight of Train B be y tons.

From the information given:
x + y = 262 ... (1)
x - y = 204 ... (2)

Adding equations (1) and (2), we get:
2x = 466
x = 233

Substitute x = 233 back into equation (1):
233 + y = 262
y = 29

So the weight of Train A is 233 tons and the weight of Train B is 29 tons.

I can confirm that the weights of Train A and Train B are indeed 233 tons and 29 tons, respectively.

Answer 5

To solve the system of equations using the addition method, we need to have the same coefficient for either x or y in both equations. Let's find a common multiplier for either x or y:

Original Equations:
1) x - 2.8y = 0.6
2) -x + 3.9y = -2.8

In order to use the addition method, let's find a common multiple of 2.8 and 3.9. The common multiple is 14.

Now, we will multiply equation (1) by 3.9 and equation (2) by 2.8 to eliminate x:

3.9(x - 2.8y) = 3.9(0.6)
-2.8(-x + 3.9y) = -2.8(-2.8)

Expanding and simplifying:
3.9x - 10.92y = 2.34
-2.8x + 10.92y = 7.84

Now, we will add the two equations:
3.9x - 10.92y - 2.8x + 10.92y = 2.34 + 7.84
1.1x = 10.18
x = 10.18 / 1.1
x = 9.25

Now, substitute x back into the first equation:
9.25 - 2.8y = 0.6
-2.8y = - 8.65
y = -8.65 / -2.8
y = 3.089

Therefore, the solution to the system of equations is (9.25, 3.089).