Question

Решите В первом вагоне груза в 1 1/3 раза больше,чем во втором.Если у первого вагона снять 11 3/4т,а во второй добавить 3 1/4т,то груза в вагонах станет поровну.Сколько груза было в каждом вагоне первоначально?

Answer 1

To solve this problem, let's assign variables to represent the initial amount of cargo in each wagon. Let's call the amount of cargo in the first wagon "x" and the amount of cargo in the second wagon "y".

According to the problem, the cargo in the first wagon is 1 1/3 times larger than the cargo in the second wagon. This can be expressed as:

x = (4/3)y

Next, we are given two conditions:

1. If 11 3/4 tons are removed from the first wagon, and 3 1/4 tons are added to the second wagon, then the amount of cargo in both wagons will be equal. 2. The amount of cargo in both wagons will be equal after the adjustments.

Let's set up an equation based on these conditions:

x - 11 3/4 = y + 3 1/4

Now, we can substitute the value of x from the first equation into the second equation:

(4/3)y - 11 3/4 = y + 3 1/4

To simplify the equation, let's convert the mixed numbers to improper fractions:

(4/3)y - (47/4) = y + (13/4)

Now, let's get rid of the fractions by multiplying both sides of the equation by 12 (the least common multiple of 3 and 4):

12 * (4/3)y - 12 * (47/4) = 12 * y + 12 * (13/4)

After simplifying, we get:

16y - 141 = 12y + 39

Next, let's isolate the variable y by subtracting 12y from both sides and adding 141 to both sides:

16y - 12y = 39 + 141

4y = 180

Dividing both sides by 4, we find:

y = 45

Now that we know the value of y, we can substitute it back into the first equation to find the value of x:

x = (4/3)y = (4/3)(45) = 60

Therefore, the initial amount of cargo in the first wagon was 60 tons, and the initial amount of cargo in the second wagon was 45 tons.

Please let me know if you have any further questions!