Question

The first barn contained 3 times more hay than the second one. After 20 tons of hay were removed from the first barn and 20 tons were added to the second barn, the amount of hay in the second barn was 5/7 of the amount remaining in the first barn. How many tons of hay was there in each barn?

Answer 1

The amount of hay in the second barn is 30 tons, and the amount of hay in the first barn is 90 tons.

Step-by-step explanation:

To solve this problem, let's first represent the amounts of hay in the two barns. Let x be the amount of hay in the second barn. Then, the amount of hay in the first barn can be represented as 3x, since it is 3 times more than the second barn.

After 20 tons of hay were removed from the first barn, the amount remaining becomes 3x - 20. After 20 tons were added to the second barn, the amount becomes x + 20.

According to the problem, the amount of hay in the second barn, x + 20, is 5/7 of the amount remaining in the first barn, 3x - 20. Setting up this equation, we have:

x + 20 = (5/7)(3x - 20)

Now we can solve for x by simplifying the equation and solving for x:

x + 20 = (15/7)x - 100/7

Let's multiply both sides by 7 to eliminate the fraction:

7(x + 20) = 15x - 100

7x + 140 = 15x - 100

Subtracting 7x from both sides, we get:

140 = 8x - 100

Adding 100 to both sides, we obtain:

240 = 8x

Dividing both sides by 8, we find that:

x = 30

Therefore, the amount of hay in the second barn is 30 tons, and the amount of hay in the first barn is 3 times that amount, which is 90 tons.

Answer 2

The solution would be like this for this specific problem:

a + 20 = 5/7 (3a - 20)
a + 20 = (15a - 100)/7
Multiply both side by 7,
7a + 140 = 15a - 100
8a = 240
a = 30

3a = 90

a + 20 = 50

3a - 20 = 70

5/7 x 70 = 50