Question

How do you find two numbers whose sum is 49, if the greater number is 4 more than 8 times the smaller number?

Answer 1

I got `44 and 5`

Explanation:

Call the numbers `x` and `y`, you get:
`x+y=49`
`x=8y+4`
substitute the second equation into the first:
`8y+4+y=49`
`9y=45`
`y=45/9=5`
so that:
`x=8*5+4=44`

Answer 2

Write two equations and solve for one variable. Then substitute the value for the first variable to find the value for the second variable.

Explanation:

The first equation would be
`x + y = 49`

Where x = the first variable
Where y = the second variable.

The second equation would be

`y = 8x + 4`

where y = the larger number.

Put `8x + 4` into the first equation in place of y this gives.

`x + 8x + 4 = 49` solve the equation for x by combining terms

`9x + 4 = 49` subtract 4 from both sides

`9x + 4 - 4 = 49 -4` this gives

`9x = 45` Divide both sides by 9 gives

`9x /9 = 45/9` The answer is

`x= 5` Now put 5 into one of the equation to find y

`y = 8(5) + 4`

`y = 44`

To check put the values into the first equation

`5 + 44 = 49`

x = 5 : y = 44