If the sum of the digits of a two-digit number is 9 and the number is 4 times th

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Question: If the sum of the digits of a two-digit number is 9 and the number is 4 times the sum of its digits, what is the number? (2021)

Options:

Correct Answer: 45

Exam Year: 2021

Solution:

Let the two-digit number be 10a + b, where a is the tens digit and b is the units digit. We have a + b = 9 and 10a + b = 4(a + b). Solving these gives a = 4 and b = 5, so the number is 45.

If the sum of the digits of a two-digit number is 9 and the number is 4 times th

Practice Questions

If the sum of the digits of a two-digit number is 9 and the number is 4 times the sum of its digits, what is the number? (2021)

Questions & Step-by-Step Solutions

If the sum of the digits of a two-digit number is 9 and the number is 4 times the sum of its digits, what is the number? (2021)

Step 1: Let the two-digit number be represented as 10a + b, where 'a' is the tens digit and 'b' is the units digit.
Step 2: According to the problem, the sum of the digits (a + b) is equal to 9.
Step 3: The problem also states that the number (10a + b) is equal to 4 times the sum of its digits (4(a + b)).
Step 4: Substitute the sum of the digits into the equation: 10a + b = 4 * 9.
Step 5: Simplify the equation: 10a + b = 36.
Step 6: Now we have two equations: a + b = 9 and 10a + b = 36.
Step 7: From the first equation (a + b = 9), we can express b as b = 9 - a.
Step 8: Substitute b in the second equation: 10a + (9 - a) = 36.
Step 9: Simplify this equation: 10a + 9 - a = 36, which becomes 9a + 9 = 36.
Step 10: Subtract 9 from both sides: 9a = 27.
Step 11: Divide both sides by 9: a = 3.
Step 12: Now substitute a back into the equation for b: b = 9 - 3 = 6.
Step 13: The digits are a = 3 and b = 6, so the two-digit number is 10a + b = 10*3 + 6 = 36.

Algebraic Representation – Understanding how to represent a two-digit number using its digits and formulating equations based on given conditions.
Digit Sum Properties – Applying properties of digit sums to solve for unknowns in a two-digit number.
Equation Solving – Solving simultaneous equations to find the values of the digits.

If the sum of the digits of a two-digit number is 9 and the number is 4 times th

What’s inside this PDF?

If the sum of the digits of a two-digit number is 9 and the number is 4 times th

Practice Questions

Questions & Step-by-Step Solutions

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