One number is one more than a second number. Three times the first is 9 less than 4 times the second. Find the numbers.

Answer 1

Let the first number be x

Let the second number be y

translate:

1) One number is one more than the second number:

x = 1+y

2) three times the first is 9 less than 4 times the second

3x = 4y - 9

once we have the two equations, we can solve for both x and y.

From eq. 1 we already know x interms of y,

x = 1+y

so we plug in 1+y in the place of x for the second equation.

so instead of 3x = 4y-9

Now it will be

3* (1+y) = 4y-9

simplify

3 + 3y = 4y - 9

collect like terms

12 = y

and from here,

x = 1+y = 1+12 = 13

The two numbers are 12 and 13

Answer 2

Suppose x is the first , y is the second

Then x = y + 1

and 3x = 4y - 9

so 3 (y +1) = 4y - 9

3y + 3 = 4y - 9

12 = y

x = 13

Check.

3 times x is 39

39 + 9 = 48

4 x 12 = 48

So it works.

Mike