algebra word problem

Question

The sum of two numbers are 100. Five times the smaller is 8 more than the larger. Find the numbers.

Answer 1

x+y =100,

lets say x is the smaller one, so: 5x= y+8------> y= 5x-8

subsitute second eq. in first one, we get: x + (5x-8) =100---->6x-8=100

6x=108------> x=108/6 =18,

x=18 so y=82

i hope it is clear

Answer 2

Hi Gin,

Let s = smaller number and l = larger number.

If the sum of both numbers is 100, then s + l = 100

If five times the smaller is 8 more than the larger, I begin to write the equation as we read it.

5x = l + 8

You have two equations:

s + l = 100 (equation 1)

5s = l + 8 (equation 2)

In the equation 2, solve for l . --> l = 5s - 8

Next, substitute 5s - 8 for variable l in the first equation. --> s + 5s - 8 = 100

Now, solve for s. --> 6s - 8 = 100

6s = 108

s = 18

Last, we can use equation 1 to solve for s by substituting 18 for s. --> 18 + l = 100

l = 82

The numbers are 82 and 18.