Question

When you reverse the digits in a certain two-digit number you decrease its value by 18. what is the number if the sum of its digits is 12?
a.92
b.75
c.45
d.86?

Answer 1

Answer: The number is 75

Lets start by defining the 2-digit number.

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Define the number
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Let x be the digit in the tens place and y be the digit in the ones place.
The number is 10x + y
The reverse of the number is 10y + x 

Now we will construct the equations needed

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Construct equations
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When the digits are reversed, the value decreases by 18:
(10x + y) - (10y + x) = 18 .    ← Apply distributive property
10x + y - 10y - x = 18            ←Combine like terms
9x - 9y = 18                           ←Divide by 9 through
x - y = 2

The sum of the digits is 12:
x + y = 12

Now that we have the two equations, we can solve for x and y.

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Solve for x and y
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x - y  = 2          ---------------------- (equation 1)
x + y = 12        ---------------------- (equation 2)

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Make x the subject in equation 1
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x - y = 2      ← Add y from both sides
    + y   +y       

x = 2 + y 

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Substitute x = 2 + y into equation 2
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x + y = 12                      ← Substitute x = 2 + y
2 + y + y = 12                ← combine like terms  
2 + 2y = 12                    ← Subtract 2 from both sides
-2           -2
2y = 10                          ← Divide by 2 on both sides
÷2    ÷2
y = 5

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Substitute y = 5 into equation 1
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x - y = 2                          ← substitute  y = 5
x - 5 = 2                          ← add 5 on both sides
   +5   +5
x = 7

Now we know the value of x and y. Lets find the 2-digit number.

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Find the 2-digit number
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The number = 10x + y = 10(7) + 5 = 75

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Answer: The number is 75
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