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If three times the larger of two numbers is divided by the smaller one, we get 4 as quotient and 3 as remainder. If seven times the smaller number is divided by the larger one, we get 5 as the quotient and 1 as the remainder. What is the smaller number?
- a)15
- b)20
- c)18
- d)25
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If three times the larger of two numbers is divided by the smaller one...
Let's assume the two numbers as follows:
Smaller number = x
Larger number = y
According to the given information:
1) "Three times the larger of two numbers is divided by the smaller one, we get 4 as quotient and 3 as remainder."
This can be expressed as:
3y ÷ x = 4 + 3/x
2) "Seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder."
This can be expressed as:
7x ÷ y = 5 + 1/y
To solve this problem, we will solve the two equations simultaneously.
Equation 1:
3y ÷ x = 4 + 3/x
Multiplying both sides by x:
3y = 4x + 3
Equation 2:
7x ÷ y = 5 + 1/y
Multiplying both sides by y:
7x = 5y + 1
Now, we have two equations:
3y = 4x + 3
7x = 5y + 1
Solving the two equations:
Multiply equation 1 by 5 and equation 2 by 4 to eliminate the coefficients of x and y:
15y = 20x + 15
28x = 20y + 4
Now, let's solve for x:
From equation 1, we have:
15y - 20x = 15 (Equation 3)
From equation 2, we have:
20y - 28x = -4 (Equation 4)
Multiply equation 3 by 2 and equation 4 by 3 to eliminate the coefficients of y and x:
30y - 40x = 30
60y - 84x = -12
Subtract equation 3 from equation 4:
60y - 84x - (30y - 40x) = -12 - 30
30y - 44x = -42 (Equation 5)
Now, let's solve equation 5 for x:
30y - 44x = -42
-44x = -30y - 42
44x = 30y + 42
11x = 7.5y + 10.5
Since the coefficients of x and y are not integers, we can conclude that this system of equations does not have an integer solution. Therefore, the given problem does not have a valid solution.
Smaller number = x
Larger number = y
According to the given information:
1) "Three times the larger of two numbers is divided by the smaller one, we get 4 as quotient and 3 as remainder."
This can be expressed as:
3y ÷ x = 4 + 3/x
2) "Seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder."
This can be expressed as:
7x ÷ y = 5 + 1/y
To solve this problem, we will solve the two equations simultaneously.
Equation 1:
3y ÷ x = 4 + 3/x
Multiplying both sides by x:
3y = 4x + 3
Equation 2:
7x ÷ y = 5 + 1/y
Multiplying both sides by y:
7x = 5y + 1
Now, we have two equations:
3y = 4x + 3
7x = 5y + 1
Solving the two equations:
Multiply equation 1 by 5 and equation 2 by 4 to eliminate the coefficients of x and y:
15y = 20x + 15
28x = 20y + 4
Now, let's solve for x:
From equation 1, we have:
15y - 20x = 15 (Equation 3)
From equation 2, we have:
20y - 28x = -4 (Equation 4)
Multiply equation 3 by 2 and equation 4 by 3 to eliminate the coefficients of y and x:
30y - 40x = 30
60y - 84x = -12
Subtract equation 3 from equation 4:
60y - 84x - (30y - 40x) = -12 - 30
30y - 44x = -42 (Equation 5)
Now, let's solve equation 5 for x:
30y - 44x = -42
-44x = -30y - 42
44x = 30y + 42
11x = 7.5y + 10.5
Since the coefficients of x and y are not integers, we can conclude that this system of equations does not have an integer solution. Therefore, the given problem does not have a valid solution.
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Community Answer
If three times the larger of two numbers is divided by the smaller one...
Let the larger number be x and the smaller number be y.
Now according to question, 3x = 4y + 3
3x - 4y = 3 ...(1)
and 3 × 25 - 4y = 3
⇒ 4y = 72 ⇒ y = 18
∴ Smaller number = 18
Now according to question, 3x = 4y + 3
3x - 4y = 3 ...(1)
and 3 × 25 - 4y = 3
⇒ 4y = 72 ⇒ y = 18
∴ Smaller number = 18
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If three times the larger of two numbers is divided by the smaller one, we get 4 as quotient and 3 as remainder. If seven times the smaller number is divided by the largerone, we get 5 as the quotient and 1 as the remainder. What is the smaller number?a)15b)20c)18d)25Correct answer is option 'C'. Can you explain this answer?
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