Linear equations with one variable on both sides reducible to linear form

Question

A two digit number is 2 more than 5 times the sum of its digits. If the digit in the tens place is 1 less than the digit in the units place, find the number.

Answer 1

Hi Shreesha,

We can approach this problem with the following 3-step approach:

Step 1) Identify the unknown variables

Step 2) Create a linear system of equations

Step 3) Solve the system of equations

Step 1) Identify unknown variables

We have 3 unknowns here:

1) The digit in the tens place (we will call it x)

2) The digit in the units place (we will call it y)

3) The two-digit number we care about (we will call it z)

Step 2) Create a linear system of equations

We will use the given information to generate 3 equations

Given info 1: The two-digit number (z) is 2 more than 5 times the sum of its digits (x and y)

Equation 1: z = 2 + 5*(x + y)

Given info 2: The digit in the tens place (A) is 1 less than the digit in the units place (y)

Equation 2: x = y - 1

Given info 3: We can use a bit of cleverness to create a third piece of information - We know that if we subtract 10 times the digit in the tens place (x) from the two-digit number (z), we will get the number in the units place (y). (For example - if our number is 54, then 54 - 50 = 4)

Equation 3: z - 10*x = y

Now, we have our 3 Equations:

Equation 1: z = 2 + 5*(x + y)

Equation 2: x = y - 1

Equation 3: z - 10*x = y

Step 3) Solve!!

Use the method with which you are most comfortable to solve the system of equations.

I hope this helps! Please let me know if you have any other questions.