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When one-third of a number is increased by 10, the result is 65. Find the sum of the digits of the original number.
9
14
11
12
12
Subtract 10 from 65 to get 55, then multiply by 3 to get the number 165 directly. Add the digits 1+6+5=12 without writing full equations.
One-third of a number (let it be x) added to 10 equals 65.
3xтАЛ+10=65
Subtract 10 from 65 to get 55, then multiply by 3 to get the number 165 directly. Add the digits 1+6+5=12 without writing full equations.
Many students calculate the number 165 correctly but stop there, forgetting the final instruction to find the sum of the digits.
Formulate the Equation
Let the number be x. According to the problem, one-third of x increased by 10 is 65.
3xтАЛ+10=65
Isolate the fraction
Subtract 10 from both sides of the equation.
3xтАЛ=65тИТ10=55
Solve for the original number
Multiply both sides by 3 to find x.
x=55├Ч3=165
Calculate the sum of digits
Sum the digits of the original number 165.
1+6+5=12
D is correct because the original number is 165, and the sum of its digits 1+6+5 is 12.
Questions involving 'sum of digits' are common in number system problems; always re-read the final sentence to ensure you aren't just finding the number itself but performing the requested secondary operation.
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