The product of a two-digit number and its tens digit is 105. Find the numbers if its ones digit is 2 more than its tens digit.
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The product of a two-digit number and its tens digit is 105. Find the numbers if its ones digit is 2 more than its tens digit.
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Problem: The product of a two-digit number and its tens digit is 105. Find the numbers if its ones digit is 2 more than its tens digit.
Solution: Represent x and y as the tens and ones digit respectively. Make two equations of the given statement.
[tex] \red{Eq. \: 1}[/tex]We can represent the two-digit number as (10x + y) since x is a face value of tens which is multiplied to 10, then add y which is the ones. This two-digit will be multiplied to x to get a product of 105 as it was said to the statement.
[tex] \red{Eq. \: 2}[/tex] y is said to be the sum of x and 2.
- Substitute y from the second equation to the first equation in terms of x.
- Solve the quadratic equation in the first equation by using the quadratic formula. Make sure that gives the positive solution.
- The tens digit of the two digit number is 3. Then, substitute it to the second equation to find the ones digit
- Thus, the ones digit of the two digit number is 5. Now, find the two-digit number.
- Therefore, the two digit number and its tens digit that has a product of 105 is:
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