Question

The sum of two numbers is 56. The difference of the two numbers is 38. What are the two numbers. Let be the larger number and y be the smaller number. Write an equation that expresses the information in the sentence "The sum of two numbers is 56" Write an equation that expresses the information in the sentence "The difference of the two numbers is 38.^ +1 Box Solve the system you have written above. The larger number , is The smaller number , y is

Answer 1

Given -

The sum of two numbers = 56

The difference of the two numbers = 38

To Find -

Write an equation that expresses the information:

"The sum of two numbers is 56"

"The difference of the two numbers is 38"

The larger number (x) =?

The smaller number (y) =?

Step-by-Step Explanation -

Let the two numbers be x and y.

So,

According to the statements:

x + y = 56 ......(i)

x - y = 38 .....(ii)

Simply add (i) and (ii):

x + y + x - y = 56 + 38

2x = 94

x = 94/2

x = 47

Put x = 47 in (i)

47 + y = 56

y = 56 - 47

y = 9

Final Answer -

"The sum of two numbers is 56"

= x + y = 56

"The difference of the two numbers is 38"

= x - y = 38

The larger number (x) = 47

The smaller number (y) = 9