- consecutive number

- digits

**Problem **(page 442)

The units digit of a two digit number is 2 more than the tens digit. If the digits are reversed, the new number is 39 less than twice the original number.

**25**

In the case above, the units digit is 3 more than the tens digit.

To solve the problem, we need to create a dictionary.

Original number is tens digit (t) + units digit (u) or **tu**.

*The units digit is two more than the tens digit*

u = 2 + t

*If the digits are reversed, the new number is 39 less than twice the original number*

ut = 2tu – 39

u • 10 + t = 2(10 • t + u) – 39 → 10u + t = 20t + 2u – 39

**With two equations, we can use algebra to solve for the variables**

u = 2 + t

10u + t = 20t + 2u – 39

*Substitute for u*

10(t + 2) + t = 20t + 2(t + 2) – 39

*Distribute*

10t + 20 + t = 20t + 2t + 4 + -39

*Simplify*

11t + 20 = 22t – 35

__ 55 __ = __ 11t __

11 11

t = 5

**If t = 5, this means the tens digit is 5. What is the units digit? **

u = 2 + t

u = 7

tu = 57

**Answer:** The number is 57.

*The units digit of a 2 digit number is 40% of the tens digit*

u = 0.40t

*If the digits are reversed, the resulting number is 27 less than the original number. *

ut = tu – 27, which is really

10u + t = 10t + u – 27

**The two equations to use are: **

u = 0.40t

10u + t = 10t + u – 27

*Substitute*

10 • (0.40 + t) = 10t + 0.40t – 27 → 4t + t = 0.40t – 27

*Simplify*

5t = 10.4t – 27

-5.4t = -27

t = 5

**Substitute 5 back into the equation for t**

u = .4(5)

u = 2

tu = 52

**The Magic Square**: Using each number from 1-9 only once, place each digit in a box so that the sum of every row, column, and diagonal is the same.

- CyberProf(TM)