Question

Blake thought of an even number and an odd number (both greater than 1), multiplied the two numbers together, added 6, divided by 5, and subtracted 3 to give an answer of 1. What was the odd number he started with?

Answer 1

Let the even and odd numbers be x and y respectively.

`\begin{gathered} \text{From the question,} \\ x>1 \\ y>1 \end{gathered}`

Multiply the two numbers together gives

`xy`

Added 6

`xy+6`

Divided by 5

`(xy+6)/(5)`

Subtracted 3 to give an answer 1

`(xy+6)/(5)-3\text{ = 1}`

We solve for xy

`\begin{gathered} (xy+6)/(5)=4 \\ xy+6=20 \\ xy=14 \end{gathered}`

The product of the even and odd number xy is 14.

In order to differentiate the even from the odd, we find the factors of 14

The possible factors of 14 are :

1 and 14 OR 2 and 7

From the factors, the odd number(y) can either be 1 or 7 but we were told that y>1.

Therefore, the odd number (y) we started with is 7