On the Morning Brain Teaser

We have brain teasers e-mailed to us at work now.

This morning’s question?

A certain number consists of two digits. The number is equal to five times the sum of its digits. If you add 9 to the number, the order of its digits is reversed. What is the number?

How do we solve this?

Define two variables: a and b. The two digit number would be 10a+b.

Consider the first sentence. “The number is equal to five times the sum of its two digits.”

10a+b=5(a+b)

Now we solve for a.

10a+b=5a+5b
5a=4b
a=4b/5

Consider the second sentence. “If you add 9 to the number, the order of its digits are reversed.”

10a+b+9=10b+a

Now we solve for a.

9a=9b-9
a=b-1

Now, we combine the two.

b-1=4b/5
5b-5=4b
b=5

Now, we plug b into one of our solutions for a.

a=b-1
a=5-1
a=4

Thus, our solution for the number?

10a+b
10*4+5
40+5
45

And there’s our solution. The two digit number is 45.

Add the two digits, and you get 9. Multiply that by 5, and you get 45.

Reverse the digits and you get 54, which is the number — 45 — plus 9.

Elementary! 🙂