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The ratio of two numbers is 15: 19. If a certain number is added to each term of the ratio it become 8: 9. What is the number added to each of the ratio?
- a)6
- b)15
- c)17
- d)23
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The ratio of two numbers is 15: 19. If a certain number is added to ea...
Given:
Ratio of two numbers = 15:19
New ratio after adding a certain number = 8:9
To Find:
The number that was added
Solution:
Let the two numbers be 15x and 19x.
Ratio of two numbers = 15:19
New ratio after adding a certain number = 8:9
To Find:
The number that was added
Solution:
Let the two numbers be 15x and 19x.
According to the question, the ratio of the two numbers is 15:19.
Therefore,
we can write the equation:
15x/19x = 15/19
Cross-multiplying,
we get: 15 × 19x = 19 × 15x 285x = 285x
Thus, we get x = 1.
Therefore, the two numbers are 15 and 19.
Let the number that was added be y.
The new ratio of the numbers is 8:9 after adding y.
Therefore, we can write the equation:
(15 + y)/(19 + y) = 8/9
Cross-multiplying,
we get: 9(15 + y) = 8(19 + y)
Simplifying the above equation,
we get: 135 + 9y = 152 + 8y
y = 17
Answer: The number that was added is 17.
Therefore,
we can write the equation:
15x/19x = 15/19
Cross-multiplying,
we get: 15 × 19x = 19 × 15x 285x = 285x
Thus, we get x = 1.
Therefore, the two numbers are 15 and 19.
Let the number that was added be y.
The new ratio of the numbers is 8:9 after adding y.
Therefore, we can write the equation:
(15 + y)/(19 + y) = 8/9
Cross-multiplying,
we get: 9(15 + y) = 8(19 + y)
Simplifying the above equation,
we get: 135 + 9y = 152 + 8y
y = 17
Answer: The number that was added is 17.
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Community Answer
The ratio of two numbers is 15: 19. If a certain number is added to ea...
Given:
The ratio of two numbers is 15:19.
To Find:
The number added to each term of the ratio.
Solution:
Let's assume the two numbers in the ratio are 15x and 19x, where x is a common multiple.
Step 1: Setting up the equation
When a certain number is added to each term of the ratio, it becomes 8:9. Therefore, we can set up the equation as follows:
(15x + n) / (19x + n) = 8/9
Where n is the number added to each term of the ratio.
Step 2: Solving the equation
To solve the equation, we can cross-multiply:
(15x + n) * 9 = (19x + n) * 8
Expanding both sides of the equation:
135x + 9n = 152x + 8n
Subtracting 8n from both sides:
135x + n = 152x
Subtracting 135x from both sides:
n = 17x
Step 3: Finding the value of x
Since n = 17x, we need to find the value of x in order to determine the number added to each term of the ratio.
We know that the two numbers in the ratio are 15x and 19x. Since the ratio is given as 15:19, we can set up another equation:
15x / 19x = 15 / 19
Cross-multiplying:
15x * 19 = 15 * 19x
285x = 285x
This equation is always true, which means x can be any value.
Step 4: Answer
Since x can be any value, the number added to each term of the ratio is 17x. Therefore, the correct answer is option C) 17.
The ratio of two numbers is 15:19.
To Find:
The number added to each term of the ratio.
Solution:
Let's assume the two numbers in the ratio are 15x and 19x, where x is a common multiple.
Step 1: Setting up the equation
When a certain number is added to each term of the ratio, it becomes 8:9. Therefore, we can set up the equation as follows:
(15x + n) / (19x + n) = 8/9
Where n is the number added to each term of the ratio.
Step 2: Solving the equation
To solve the equation, we can cross-multiply:
(15x + n) * 9 = (19x + n) * 8
Expanding both sides of the equation:
135x + 9n = 152x + 8n
Subtracting 8n from both sides:
135x + n = 152x
Subtracting 135x from both sides:
n = 17x
Step 3: Finding the value of x
Since n = 17x, we need to find the value of x in order to determine the number added to each term of the ratio.
We know that the two numbers in the ratio are 15x and 19x. Since the ratio is given as 15:19, we can set up another equation:
15x / 19x = 15 / 19
Cross-multiplying:
15x * 19 = 15 * 19x
285x = 285x
This equation is always true, which means x can be any value.
Step 4: Answer
Since x can be any value, the number added to each term of the ratio is 17x. Therefore, the correct answer is option C) 17.
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