Question

By placing a 2 at both ends of a number, the value of the number is increased by 2317. What is the sum of the digits of the original number?​

Answer 1

Answer:

87

Step-by-step explanation:

First, the number has to be a 2-digit number. This can easily be proven by testing using numbers.

Now that we have decided the number has 2 digits, suppose the number is XY where X is the tens and Y is the ones.

The value increases by 2785 when the digit 2 is added to both ends of the number, therefore we can conclude that

2XY2 = XY + 2785

By using the number place value, we can rearrange the equation and get

2000 + 100X + 10Y + 2 = 10X + Y + 2785

Rearranging terms

90X + 9Y = 783

Divide by 9

10X + Y = 87 = 10*8 + 7

Therefore, the number XY must be 87