Question

The sum of two numbers is 15 and their difference is 11

Answer 1

Answer:-

Sum: $\boxed{\fcolorbox{green}{yellow}{13 + 2 = 15}}$

Difference: $\boxed{\fcolorbox{green}{pink}{13 - 2 = 11}}$

step-by-step-explanation:

The Sum of Two Numbers is 15 and Their Difference is 11

Sum Difference

The sum of two numbers is 15 and their difference is 11. What are the two numbers? Let's start by calling the two numbers we are looking for x and y.

The sum of x and y is 15. In other words, x plus y equals 15 and can be written as equation A:

$\boxed{\fcolorbox{green}{yellow}{x + y = 15}}$

The difference between x and y is 11. In other words, x minus y equals 11 and can be written as equation B:

$\boxed{\fcolorbox{green}{green}{x - y = 11}}$

Now solve equation B for x to get the revised equation B:

$\boxed{\fcolorbox{green}{silver}{x - y = 11}}$

$\boxed{\fcolorbox{green}{brown}{x = 11 + y}}$

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 15

11 + y + y = 15

11 + 2y = 15

2y = 4

$\boxed{\fcolorbox{green}{gold}{y = 2}}$

Now we know y is 2. Which means that we can substitute y for 2 in equation A and solve for x:

x + y = 15

x + 2 = 15

$\boxed{\fcolorbox{green}{indigo}{X = 13}}$

Summary: The sum of two numbers is 15 and their difference is 11. What are the two numbers? Answer: 13 and 2 as proven here:

Sum: $\boxed{\fcolorbox{green}{beige}{13 + 2 = 15}}$

Difference: $\boxed{\fcolorbox{green}{orange}{13 - 2 = 11}}$

Answer 2

SOLUTION

COMPLETE QUESTION

GIVEN

• The sum of two numbers is 15

• Their difference is 11

TO DETERMINE

The numbers

EVALUATION

Let the required numbers are a and b

By condition 1 we get

a + b = 15 - - - - - - - (1)

By condition 2 we get

a - b = 11 - - - - - - -(2)

Adding Equation 1 and Equation 2 we get

2a = 26

⇒ a = 13

From Equation 1 we get

13 + b = 15

⇒ b = 15 - 13

⇒ b = 2

FINAL ANSWER

Hence the required numbers are 13 and 2

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