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The sum of the two numbers is 11 and their product is 30, then the numbers are
- a)8, 3
- b)9, 2
- c)7, 4
- d)6, 5
Correct answer is option 'D'. Can you explain this answer?
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The sum of the two numbers is 11 and their product is 30, then the num...
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The sum of the two numbers is 11 and their product is 30, then the num...
The sum of the two numbers is 11 and their product is 30, then the numbers are:
To solve this problem, we can use a system of equations. Let's denote the two numbers as x and y.
1. Set up the equations:
We are given two pieces of information:
- The sum of the two numbers is 11: x + y = 11
- The product of the two numbers is 30: xy = 30
2. Solve the system of equations:
There are several ways to solve a system of equations, but in this case, we can use substitution.
From the first equation, we can rearrange it to solve for x: x = 11 - y.
Substituting this value of x into the second equation, we get:
(11 - y)y = 30
Expanding and rearranging the equation, we have:
11y - y^2 = 30
Rearranging further, we have:
y^2 - 11y + 30 = 0
We can factor this quadratic equation:
(y - 6)(y - 5) = 0
Setting each factor equal to zero, we have two possible solutions for y:
y - 6 = 0 or y - 5 = 0
Solving these equations, we find:
y = 6 or y = 5
3. Find the values of x:
To find the corresponding values of x, we substitute the values of y back into the equation x = 11 - y.
When y = 6, x = 11 - 6 = 5.
When y = 5, x = 11 - 5 = 6.
Therefore, the two numbers that satisfy both conditions are 5 and 6.
4. Identify the correct option:
The correct option is (d) 6, 5, as these are the numbers we found in step 3 that satisfy both the sum and product conditions.
Conclusion:
The numbers that satisfy the given conditions are 6 and 5, and the correct option is (d).
To solve this problem, we can use a system of equations. Let's denote the two numbers as x and y.
1. Set up the equations:
We are given two pieces of information:
- The sum of the two numbers is 11: x + y = 11
- The product of the two numbers is 30: xy = 30
2. Solve the system of equations:
There are several ways to solve a system of equations, but in this case, we can use substitution.
From the first equation, we can rearrange it to solve for x: x = 11 - y.
Substituting this value of x into the second equation, we get:
(11 - y)y = 30
Expanding and rearranging the equation, we have:
11y - y^2 = 30
Rearranging further, we have:
y^2 - 11y + 30 = 0
We can factor this quadratic equation:
(y - 6)(y - 5) = 0
Setting each factor equal to zero, we have two possible solutions for y:
y - 6 = 0 or y - 5 = 0
Solving these equations, we find:
y = 6 or y = 5
3. Find the values of x:
To find the corresponding values of x, we substitute the values of y back into the equation x = 11 - y.
When y = 6, x = 11 - 6 = 5.
When y = 5, x = 11 - 5 = 6.
Therefore, the two numbers that satisfy both conditions are 5 and 6.
4. Identify the correct option:
The correct option is (d) 6, 5, as these are the numbers we found in step 3 that satisfy both the sum and product conditions.
Conclusion:
The numbers that satisfy the given conditions are 6 and 5, and the correct option is (d).
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The sum of the two numbers is 11 and their product is 30, then the numbers area)8, 3b)9, 2c)7, 4d)6, 5Correct answer is option 'D'. Can you explain this answer?
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The sum of the two numbers is 11 and their product is 30, then the numbers area)8, 3b)9, 2c)7, 4d)6, 5Correct answer is option 'D'. Can you explain this answer? for Teaching 2025 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about The sum of the two numbers is 11 and their product is 30, then the numbers area)8, 3b)9, 2c)7, 4d)6, 5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Teaching 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the two numbers is 11 and their product is 30, then the numbers area)8, 3b)9, 2c)7, 4d)6, 5Correct answer is option 'D'. Can you explain this answer?.
The sum of the two numbers is 11 and their product is 30, then the numbers area)8, 3b)9, 2c)7, 4d)6, 5Correct answer is option 'D'. Can you explain this answer? for Teaching 2025 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about The sum of the two numbers is 11 and their product is 30, then the numbers area)8, 3b)9, 2c)7, 4d)6, 5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Teaching 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the two numbers is 11 and their product is 30, then the numbers area)8, 3b)9, 2c)7, 4d)6, 5Correct answer is option 'D'. Can you explain this answer?.
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