word problem for system of equations

Question

The sum of the digits of a certain two-digit number is 7.  Reversing its digits increases the number by 9.  What is the number?

Answer 1

If the two-digit number can be represented as follows: 'ab'

 

Then the sum of the digits of a certain two-digit number is 7. 

a + b = 7

 

So we can find pairs of numbers that add up to 7.

1 and 6

2 and 5

3 and 4

 

Reversing its digits increases the number by 9.
'ba' = 'ab' + 9

 

METHOD 1: Guess and Check

 

Using the three different combinations, you can arrive at the correct answer.

 

METHOD 2: System of equations

 

We can rewrite the equation: 'ba' = 'ab' + 9 in a more appropriately as

 

(10b + a) = (10a + b) + 9

a + b = 7

 

Two equations, two unknowns. Solve algebraically.

 

Answer 2

9a - 9b = -9

 

  a + b  = 7

 

Reduce the first equation dividing by 9.

 

a - b = -1

 

a + b = 7

 

 

Solve by elimination by adding the two equations together.

 

2a = 6

 

Divide both sides of the equation by 2

 

a = 3

 

Now substitute this value for a into the second equation

 

3 + b = 7

 

b = 4

 

Therefore, your answers are a=3 and b=4.

 

Good luck with the rest of your problems.

 

 

regards,

 

Shanthikumar Mayuran