The value of a number whose units digit is x and whose tens digit is three more than the units digit.

Question

Translate into an algebraic expression and simplify if possible.

Answer 1

Let's begin with an example of any number that could fit this expression.

Let's try 74.

1. 4 is the units digit in 74. Thus x = 4. x = units digit.
2. The tens digit is 7 which is 3 more than 4. The tens digit can be written as x + 3.
3. The value of 74 could be expressed as 10(x+3) + x. We multiply the tens digit by 10 to get its value. In this case it's is 10(4+3), which gives us 70 and then we add the units digit (4) to get 74.
4. The expression 10(x+3) + x is simplified as 10x + 30 + x, which is further simplifies to 11x+30.

Let's try another example to see if this is true. We need another example of a two digit number where the tens digit is 3 more than the ones digit. How about 41?

1. The x is 1 since it's in the ones digit.
2. Let's plug x =1 into 11x + 30 and see if we get 41. 11(1) +30 = 11 + 30 = 41. It worked!

Let's do one more example to really make sure this is true. How about 85?

1. The x is 5 since it's in the ones digit.
2. Let's plug x = 5 into 11x + 30 and see if we get 85. 11(5) + 30 = 55 + 30 = 85. It worked! I'm convinced. Try some examples of your own!

I hope this helped! If you need more algebra tutoring, I would be happy to provide individual tutoring in Algebra. :)