Question

The larger of 2 numbers is one less than 8 times the smaller. Their sum is 179. Find the numbers

Answer 1

greater = x = 159

smaller = y = 20

Explanation:

Let:

Number 1 = x (greater)

Number 2 = y (smaller)

Now according to given conditions:

x = 8y -1 ................. eq 1

x + y = 179 ................ eq 2

By taking eq 1:

x = 8y -1

Subtracting 8y from both sides:

x - 8y = 8y -8y -1

after cancellation of same terms with opposite signs

x - 8y = -1 .................... eq 3

Subtracting eq 3 from eq 2

(x + y) - (x - 8y)= 179 - (-1)

As "-" into "-" gives "+"

x + y - x + 8y = 179 + 1

after cancellation of same terms with opposite signs and adding same terms:

9y = 180

Dividing both sides by 9 we get

y = 180/9

y = 20

Putting value of y in eq 2 we get:

x + y = 179

x + 20 = 179

Subtracting 20 from both sides

x = 179 - 29

x = 159

So the numbers are:

greater = x = 159

smaller = y = 20

I hope it will help you!