Math / Algebra

Question18
Select the correct answer from the drop-down menu.
In a two-digit number, the tens digit is twice the ones digit. The difference of the ones digit and half the tens digit is 0 . An equation created to find the digit in the ones place will have $\square$

Studdy Solution

STEP 1

What is this asking? We need to figure out what the ones digit is in a two-digit number where the tens digit is double the ones digit, and the ones digit minus half the tens digit equals zero.
Then, we need to describe how many solutions the equation used to find the ones digit will have. Watch out! Don't mix up the tens and ones digits!
Also, make sure to interpret the relationship between the digits correctly.

STEP 2

1. Set up variables
2. Create an equation
3. Analyze the equation

STEP 3

Let's call the tens digit $t$ and the ones digit $o$ .
This will help us keep things organized!

STEP 4

We know the tens digit ( $t$ ) is twice the ones digit ( $o$ ).
We can write that as an equation: $t = 2 \cdot o$ .
This tells us how the digits relate to each other!

STEP 5

We also know that the difference between the ones digit ( $o$ ) and half the tens digit ( $t/2$ ) is 0.
We can write that as another equation: $o - \frac{t}{2} = 0$ .
This gives us another perspective on the relationship!

STEP 6

Now, let's substitute the first equation ( $t = 2 \cdot o$ ) into the second equation.
We're doing this to get an equation with just one variable, making it easier to solve.
Replacing $t$ with $2 \cdot o$ in the second equation gives us $o - \frac{2 \cdot o}{2} = 0$ .

STEP 7

Let's simplify this new equation.
Dividing $2 \cdot o$ by $2$ gives us $o$ .
So, the equation becomes $o - o = 0$ .

STEP 8

Our simplified equation, $o - o = 0$ , can also be written as $0 = 0$ .
This is a special kind of equation!
It's always true, no matter what value $o$ takes.
This means there are infinitely many solutions for $o$ .
However, since $o$ represents a digit in a two-digit number, it must be a whole number between 0 and 9 inclusive.
This gives us 10 possible solutions for $o$ : 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
For each of these values of $o$ , there's a corresponding value for $t$ that satisfies our initial conditions.

STEP 9

The equation to find the ones digit, $0 = 0$ , has infinitely many solutions in general, but only 10 possible solutions in our context (0 through 9).
Since the problem asks for "an" equation, we can use the simplified equation $0 = 0$ , which has infinitely many solutions.
So, the dropdown answer is "infinitely many".

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Question18
Select the correct answer from the drop-down menu.
In a two-digit number, the tens digit is twice the ones digit. The difference of the ones digit and half the tens digit is 0 . An equation created to find the digit in the ones place will have $\square$

Studdy Solution

STEP 1

STEP 2

1. Set up variables
2. Create an equation
3. Analyze the equation

STEP 3

Let's call the tens digit $t$ and the ones digit $o$ .
This will help us keep things organized!

STEP 4

We know the tens digit ( $t$ ) is twice the ones digit ( $o$ ).
We can write that as an equation: $t = 2 \cdot o$ .
This tells us how the digits relate to each other!

STEP 5

We also know that the difference between the ones digit ( $o$ ) and half the tens digit ( $t/2$ ) is 0.
We can write that as another equation: $o - \frac{t}{2} = 0$ .
This gives us another perspective on the relationship!

STEP 6

Now, let's substitute the first equation ( $t = 2 \cdot o$ ) into the second equation.
We're doing this to get an equation with just one variable, making it easier to solve.
Replacing $t$ with $2 \cdot o$ in the second equation gives us $o - \frac{2 \cdot o}{2} = 0$ .

STEP 7

Let's simplify this new equation.
Dividing $2 \cdot o$ by $2$ gives us $o$ .
So, the equation becomes $o - o = 0$ .

STEP 8

STEP 9

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Question18Select the correct answer from the drop-down menu.In a two-digit number, the tens digit is twice the ones digit. The difference of the ones digit and half the tens digit is 0 . An equation created to find the digit in the ones place will have □\square□

Studdy Solution

STEP 1

STEP 2

1. Set up variables2. Create an equation3. Analyze the equation

STEP 3

Let's call the tens digit ttt and the ones digit ooo.This will help us keep things organized!

STEP 4

We know the tens digit (ttt) is twice the ones digit (ooo).We can write that as an equation: t=2⋅ot = 2 \cdot ot=2⋅o.This tells us how the digits relate to each other!

STEP 5

We also know that the difference between the ones digit (ooo) and half the tens digit (t/2t/2t/2) is 0.We can write that as another equation: o−t2=0o - \frac{t}{2} = 0o−2t​=0.This gives us another perspective on the relationship!

STEP 6

STEP 7

Let's simplify this new equation.Dividing 2⋅o2 \cdot o2⋅o by 222 gives us ooo.So, the equation becomes o−o=0o - o = 0o−o=0.

STEP 8

STEP 9

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question18
Select the correct answer from the drop-down menu.
In a two-digit number, the tens digit is twice the ones digit. The difference of the ones digit and half the tens digit is 0 . An equation created to find the digit in the ones place will have $\square$

1. Set up variables
2. Create an equation
3. Analyze the equation

Let's call the tens digit $t$ and the ones digit $o$ .
This will help us keep things organized!

We know the tens digit ( $t$ ) is twice the ones digit ( $o$ ).
We can write that as an equation: $t = 2 \cdot o$ .
This tells us how the digits relate to each other!

We also know that the difference between the ones digit ( $o$ ) and half the tens digit ( $t/2$ ) is 0.
We can write that as another equation: $o - \frac{t}{2} = 0$ .
This gives us another perspective on the relationship!

Let's simplify this new equation.
Dividing $2 \cdot o$ by $2$ gives us $o$ .
So, the equation becomes $o - o = 0$ .