Question

The difference between two num-

bers is 24. What are the numbers
if their sum is 78?
(Please help me!)

Answer 1

The numbers are 27 and 51

Explanation

x - y = 24

x + y = 78

Add together the equations

2x = 102

x = 51

Put into equation

51 - y = 24

27 = y

Answer 2

51 and -27

Explanation:

The sum of two numbers is 24 and their difference is 78. 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 24. In other words, x plus y equals 24 and can be written as equation A:

x + y = 24

The difference between x and y is 78. In other words, x minus y equals 78 and can be written as equation B:

x - y = 78

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

x - y = 78

x = 78 + y

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

x + y = 24

78 + y + y = 24

78 + 2y = 24

2y = -54

y = -27

Now we know y is -27. Which means that we can substitute y for -27 in equation A and solve for x:

x + y = 24

x + -27 = 24

X = 51

Summary: The sum of two numbers is 24 and their difference is 78. What are the two numbers? Answer: 51 and -27 as proven here:

Sum: 51 + -27 = 24

Difference: 51 - -27 = 78