Question

The product of two integers is 150. One integer is 5 less than twice the other. How do you find the integers?

Answer 1

The integers are `color(green)(10)` and `color(green)(15)`

Explanation:

Let the integers be `a` and `b`
We are told:
`color(white)("XXX")a * b =150`
`color(white)("XXX")a=2b-5`

Therefore
`color(white)("XXX")(2b-5) * b =150`

After simplifying
`color(white)("XXX")2b^2-5b-150=0`

Factoring
`color(white)("XXX")(2b+15)*(b-10)=0`

`{:(2b+15=0," or ",b-10=0),(rarrb=15/2,,rarr b=10),("impossible",,),("since b integer",,):}`

So `b=10` and since `a=2b-5 rarr a=15`