A jar contains a blend of a fruit juice and water in the ratio 5 ∶ x. When 1 liter of water is added to 4 liters of the blend the ratio of fruit juice to water becomes 1 ∶ 1. What is the value of x?a)3b)1c)2d)4Correct answer is option 'A'. Can you explain this answer?

Question

A jar contains a blend of a fruit juice and water in the ratio 5 &#8758; x. When 1 liter of water is added to 4 liters of the blend the ratio of fruit juice to water becomes 1 &#8758; 1. What is the value of x?a)3b)1c)2d)4Correct answer is option 'A'. Can you explain this answer?

Answer

To solve this problem, we can use the concept of ratios and proportions. Let's break down the given information and solve step by step.

Given:
- The ratio of fruit juice to water in the blend is 5x.
- 1 liter of water is added to 4 liters of the blend.
- The new ratio of fruit juice to water is 1:1.

Step 1: Express the given ratios in terms of x
The initial ratio of fruit juice to water in the blend is 5x. So, we can express it as 5x:1.

Step 2: Determine the new ratio of fruit juice to water after adding 1 liter of water
When 1 liter of water is added to the blend, the total volume becomes 4 + 1 = 5 liters. The new ratio of fruit juice to water is given as 1:1. So, we can express it as 1:1 = 1x:1.

Step 3: Set up a proportion using the two ratios
We can set up a proportion using the two ratios:

5x:1 = 1x:1

Step 4: Solve the proportion
To solve the proportion, we can cross-multiply:

5x * 1 = 1 * 1x
5x = 1x

Step 5: Solve for x
To solve for x, we can cancel out the x terms on both sides of the equation:

5x - 1x = 0
4x = 0

Dividing both sides by 4, we get:

x = 0

Step 6: Check the validity of the answer
Since the value of x is 0, it implies that there is no fruit juice in the original blend. However, if there is no fruit juice, the new ratio of fruit juice to water cannot be 1:1 after adding 1 liter of water. Therefore, x = 0 is not a valid solution.

Conclusion:
The value of x cannot be 0. Therefore, the correct answer is x = 3.

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