In a certain mixture, the ratio of two components is 2:3. If 5 liters of the first component is added, what will be the new ratio if the initial volume of the second component was 15 liters?
Practice Questions
1 question
Q1
In a certain mixture, the ratio of two components is 2:3. If 5 liters of the first component is added, what will be the new ratio if the initial volume of the second component was 15 liters?
1:3
2:3
3:2
2:5
Let the initial amounts be 2x and 3x. After adding 5 liters to the first component, the new ratio becomes (2x + 5):3x. Solving gives 3:2.
Questions & Step-by-step Solutions
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Q
Q: In a certain mixture, the ratio of two components is 2:3. If 5 liters of the first component is added, what will be the new ratio if the initial volume of the second component was 15 liters?
Solution: Let the initial amounts be 2x and 3x. After adding 5 liters to the first component, the new ratio becomes (2x + 5):3x. Solving gives 3:2.
Steps: 10
Step 1: Identify the initial ratio of the two components, which is 2:3.
Step 2: Let the initial amounts of the components be represented as 2x for the first component and 3x for the second component.
Step 3: Since the initial volume of the second component is given as 15 liters, we can set 3x = 15.
Step 4: Solve for x by dividing both sides of the equation by 3: x = 15 / 3 = 5.
Step 5: Now, calculate the initial amount of the first component: 2x = 2 * 5 = 10 liters.
Step 6: Add 5 liters to the first component: 10 liters + 5 liters = 15 liters.
Step 7: The amount of the second component remains the same at 15 liters.
Step 8: Now, we have 15 liters of the first component and 15 liters of the second component.
Step 9: Write the new ratio of the first component to the second component: 15:15.
