The difference of the two integers is 9. five times the smaller is 9 more than three times the larger. find the integers.

2
by Pixieee

2014-11-04T22:41:32+08:00
Larger number = 27

smaller number = 18
2014-11-06T14:07:37+08:00
Simple math

Let x be the smaller integer and y the larger integer

So the first equation will be like this

y - x = 9

and the second will be

5x = 9 + 3y

Let's compute for y using the first equation

y - x = 9

move y to the right and change sign

y = x + 9

Let''s now use x here to replace x in the second equation

5x = 9 + 3(x + 9)

Multiply

5x = 9 + 3x + 27

5x = 3x + 36

Move 3x to the left and change sign

5x - 3x = 36

Subtract

2x = 36

Divide by 2 to eliminate the 2 in the 2x

2x/2 = 36/2

x = 18

Let us now use the value of y to know the real value of x in the first equation.

y = x + 9

y = 18 + 9

y = 27

Let's check

y - x = 9

27 - 18 = 9

9 = 9 correct

Let's use the second equation

5x = 9 + 3y

5(18) = 9 + 3(27)

90 = 9 + 81

90 = 90 correct

I hope it helps