the difference between the digits in two-digit numeral is 3. the units' digits is twice the tens's digit. Find the numeral.

Question

To solve word problems involving two-digit numerals.

Answer 1

Hey Chiara! This can be a tricky word question because it requires understanding of absolute value and also dealing with two unknowns. Guess what? We can solve this! So don't get discouraged.

First let me make sure I understand the question. If the question is: "The difference between the digits in a two-digit numeral is 3. The units' digit is twice the tenths' digit. Find the numeral." Then here is the solution:

 

Step 1: Let's give names to our unknowns.

Our unknowns are: the number in units' digit, and the number in tenths' digit.

So let's assume the two-digit number is xy.

 

Step 2: From the question, we know |x - y| = 3, 

Please note that the absolute value means that we don't care about a negative number appearing in x-y. In other words we only care about the magnitude and not the direction.

 

Step 3: Also from the question, we know 2x = y.

We are in luck! Since we can solve a problem with 2 equations, and 2 variables.

 

Step 4: Let's match up the corresponding values of both equations so we can eliminate one unknown:

Plan&Technique: First, let's rearrange 2x = y to get 2x-y = 0, so it will leave us with a "-y" and we can then eliminate the y variable by subtracting both equations.

Now we get:

2x-y = 0

x - y = 3

Let's subtract corresponding values from equations, and we get, x = -3

NOTE: Remember we are using absolute value, so we care only about the magnitude, and we ignore the "negative" sign.

So we can convert it to x=3.

(Rationale for absolute value: we cannot have a two digit number like "4-8", but instead we can have a two-digit number like "48". We can also have a number "-48" but that is beyond the scope of this question, since we are more concerned about what is in the units' digit.)

Then we can plug x=3 into y = 2x, and we get y = 2*3 = 6.

So x is 3, and y is 6.

Answer: The two-digit number is 36.

Hope this helps Chiara. Have a lovely day.

Answer 2

 

The 2-digit number is  10a+b

The unit's digit is twice the ten's digit:  b=2a

The difference between the digits is 3:  b-a = 3   (we know b>a  because b=2a, otherwise we'd have used absolute value)

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Can you put these together and solve for a?  Once you know a you can find b (and vice-versa if you choose to find b first).