Question

It is necessary to pour grape juice into jars with a capacity of 2 liters or 3 liters. If you pour juice into jars with a capacity of 2 liters, then you will need 2 more jars than jars with a capacity of 3 liters. How many liters of grape juice should be poured?

Answer 1

Ответ:12 liters

Пошаговое объяснение:

Answer 2

Let's solve this problem step by step.

Let's assume the number of jars with a capacity of 2 liters is x. And let's assume the number of jars with a capacity of 3 liters is y.

According to the given information, we can write two equations:

Equation 1: x = y + 2 (If juice is poured into jars with a capacity of 2 liters, then you will need 2 more jars than jars with a capacity of 3 liters.)

Equation 2: 2x + 3y = total amount of grape juice (Since the total capacity of all jars combined should be equal to the amount of grape juice poured.)

To find the total amount of grape juice, we need to solve these equations simultaneously.

Now, let's substitute the value of x from Equation 1 into Equation 2:

2(y + 2) + 3y = total amount of grape juice

Simplifying the equation:

2y + 4 + 3y = total amount of grape juice

5y + 4 = total amount of grape juice

Now, let's solve for y:

5y = total amount of grape juice - 4

y = (total amount of grape juice - 4) / 5

Since the number of jars must be a whole number, the total amount of grape juice minus 4 must be divisible by 5.

Next, let's substitute the value of y into Equation 1:

x = y + 2 x = [(total amount of grape juice - 4) / 5] + 2

Now, we need to find a solution where both x and y are whole numbers, as they represent the number of jars. We can test different values for the total amount of grape juice and check if the resulting x and y values are whole numbers.

For example, if we assume the total amount of grape juice is 23 liters, we can substitute it into the equations:

y = (23 - 4) / 5 y = 19 / 5 y = 3.8 (not a whole number)

Since y is not a whole number, we can conclude that 23 liters is not the correct solution.

We need to continue this process by testing different values for the total amount of grape juice until we find a solution where both x and y are whole numbers.

Unfortunately, based on the information provided, we cannot determine the exact amount of grape juice that needs to be poured into the jars. The problem lacks sufficient information to find a unique solution.