Applying Systems of Linear Equations Part One

[Chocolate]

A number consists of two digits whose sum is 11. If the digits were reversed, the original number is increased by 27. The original number is _____ .

 

[stapel]

Pick variables for the two digits; say, "a" and "b", so the original number is 10a + b. Form an equation that represents the digit sum.

Write an expression that represents the number formed when the digits are reversed. Then translate "(new number) is (old number) plus (twenty-seven)" into an equation.

Solve the system of equations.

Eliz.

 

[ting]

Let the two digits be x and y, there sum is 11.

x + y = 11 [1]


If the digits were reversed, the original number is increased by 27.


10y + x = 10x + y + 27 [2]

Rearrange [2] and mulyiply [1] by 9

9y - 9x = 27 [3]

9y + 9x = 99


Eliminate x by addition to find y, then find x.


Edit: After reading Denis' post.


Of course you wouldn't mutilpy [1] by 9, you'd divide [3] by 9

Giving

y - x = 3

y + x =11

Then find x by elimination or otherwise.

Can you find the two numbers?

 

[Denis]

A number consists of two digits whose sum is 11. If the digits were reversed, the original number is increased by 27. The original number is _____ .

With a 2digit number, if we let 1st digit = a and 2nd digit = b, then the
2 digit number = 10a + b; as example, take 57: 10(5) + 7 = 50 + 7 = 57 ; follow that?

With yours, we have a + b = 11; so a = 11 - b [1]

The number = 10a + b
The number reversed = 10b + a

So 10b + a - (10a + b) = 27
10b + a - 10a - b = 27
9b - 9a = 27
b - a = 3 [2]

Now substitute [1] in [2]: can you finish it off ?