Question

The sum of two numbers is 43, and their differences is 7​

Answer 1

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The sum of two numbers is 43 and their difference is 7. 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 43. In other words, x plus y equals 43 and can be written as equation A:

x + y = 43

The difference between x and y is 7. In other words, x minus y equals 7 and can be written as equation B:

x - y = 7

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

x - y = 7

x = 7 + y

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

x + y = 43

7 + y + y = 43

7 + 2y = 43

2y = 36

y = 18

Now we know y is 18. Which means that we can substitute y for 18 in equation A and solve for x:

x + y = 43

x + 18 = 43

X = 25

Summary: The sum of two numbers is 43 and their difference is 7. What are the two numbers? Answer: 25 and 18 as proven here:

Sum: 25 + 18 = 43

Difference: 25 - 18 = 7

Answer 2

Explanation:

Let the numbers be x and y. Then x + y = 43 and x - y = 7.

Solve this system of linear equations by addition/subtraction:

x + y = 43

x - y = 7

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2x = 50, so x must be 25. Since x - y = 7, 25 - y = 7 and y = 18.

Check: 25 + 18 = 43 (correct); 25 - 18 = 7 (correct)