If the sum of two numbers is 30 and their difference is 10, what are the numbers

₹0.0

Question: If the sum of two numbers is 30 and their difference is 10, what are the numbers?

Options:

Correct Answer: 20 and 10

Solution:

Let the numbers be x and y. We have x + y = 30 and x - y = 10. Solving these gives x = 20 and y = 10.

If the sum of two numbers is 30 and their difference is 10, what are the numbers?

If the sum of two numbers is 30 and their difference is 10, what are the numbers?

Step 1: Let the two numbers be x and y.
Step 2: Write down the first equation based on the sum of the numbers: x + y = 30.
Step 3: Write down the second equation based on the difference of the numbers: x - y = 10.
Step 4: Now we have two equations: x + y = 30 and x - y = 10.
Step 5: To solve for x, we can add the two equations together: (x + y) + (x - y) = 30 + 10.
Step 6: This simplifies to 2x = 40.
Step 7: Divide both sides by 2 to find x: x = 20.
Step 8: Now that we have x, we can find y by substituting x back into one of the original equations. Use x + y = 30.
Step 9: Substitute x = 20 into the equation: 20 + y = 30.
Step 10: Solve for y by subtracting 20 from both sides: y = 30 - 20.
Step 11: This gives us y = 10.
Step 12: The two numbers are x = 20 and y = 10.

Algebraic Equations – The question tests the ability to set up and solve a system of linear equations.
Word Problems – The question requires translating a verbal problem into mathematical equations.