Respuesta :
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
--------------------------------------------------------------
Lets start by defining the 2-digit number.
--------------------------------------------------------------
Define the number
--------------------------------------------------------------
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
--------------------------------------------------------------
Construct equations
--------------------------------------------------------------
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.
--------------------------------------------------------------
Solve for x and y
--------------------------------------------------------------
x - y = 2 ---------------------- (equation 1)
x + y = 12 ---------------------- (equation 2)
--------------------------------------------------------------
Make x the subject in equation 1
--------------------------------------------------------------
x - y = 2 ← Add y from both sides
+ y +y
x = 2 + y
--------------------------------------------------------------
Substitute x = 2 + y into equation 2
--------------------------------------------------------------
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
--------------------------------------------------------------
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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