Question

the sum of two numbers is 45. the greater number is 9 more than the other number. Find each number. use a system of linear equations to justify your answer

Answer 1

Let x and y be the numbers that sum up to 45.

Note that:

• x + y = 45
• y + 9 = x

Simplify the second equation such that the constant is the subject.

• y + 9 = x
• => -x + y = -9

Use system of equations to solve for both variables.

• x + y = 45

-x + y = -9

• => 2y = 36
• => y = 18

Substitute the value of y into the second equation to find x.

• y + 9 = x
• => 18 + 9 = x
• => 27 = x

The value of x and y is 27 and 18 respectively.

Answer 2

18 and 27

Explanation:

Let x = first (smaller) number

Let y = second (larger) number

Sum of two numbers is 45:

⇒ x + y = 45

The greater number is 9 more than the other number:

⇒ y = x + 9

Substitute y = x + 9 into x + y = 45 and solve for x:

⇒ x + (x + 9) = 45

⇒ 2x + 9 = 45

⇒ 2x = 36

⇒ x = 18

Substitute found value for x into y = x + 9 and solve for y:

⇒ y = 18 + 9

⇒ y = 27

Therefore, the two numbers are 18 and 27