Finding the Fourth Number: Maintaining Average in Sequence 5,7,3

Q: What if I add a number larger than 5?

If you add a number larger than 5 (like 7 or 15), it will pull the average upward. If you add a number smaller than 5 (like 0 or 4), it will pull the average downward.

Q: How do I remember the formula for this type of problem?

Remember: $ \text{Average} = \frac{\text{Sum of all numbers}}{\text{Count of numbers}} $When adding one more number, your new count increases by 1, and your new sum increases by that number!

Q: What happens if I pick one of the wrong answer choices?

If x = 0: New average = $ \frac{15+0}{4} = 3.75 $ (too low!)If x = 4: New average = $ \frac{15+4}{4} = 4.75 $ (still too low!)If x = 15: New average = $ \frac{15+15}{4} = 7.5 $ (way too high!)

Average Calculations with Fourth Value

Look at the following numers:

$5,7,3$

Which number can be added to the group so that its average does not change?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 What number can be added to the group without changing the average

00:03 Let's start by calculating the original average

00:07 To calculate the average, we'll sum and divide by the number of occurrences

00:19 This is the original average, now let's add any number and check

00:27 We'll use the formula for calculating average to find the new average

00:46 This average is not equal to the original, let's try the next number

00:56 We'll use the formula for calculating average to find the new average

01:15 This average equals the original, let's try the next number

01:22 We'll use the formula for calculating average to find the new average

01:37 This average is not equal to the original

01:41 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following numers:

$5,7,3$

Which number can be added to the group so that its average does not change?

Step-by-step solution

To solve this problem, let's follow these concise steps:

Step 1: Calculate the current average of the given numbers 5, 7, and 3.

The sum of the numbers is $5 + 7 + 3 = 15$ .
The count of numbers is 3.
Thus, the average is $\frac{15}{3} = 5$ .

Step 2: Set up an equation with an additional number, $x$ , so that the average remains the same.

Adding a fourth number, $x$ , gives us a new set of numbers: 5, 7, 3, and $x$ .
The new average should still be 5, so:

$\frac{5 + 7 + 3 + x}{4} = 5$

**Step 3: Solve the equation for $x$ .

Calculate the left side: $5 + 7 + 3 + x = 15 + x$ .
Set up the equation: $\frac{15 + x}{4} = 5$ .

Multiply both sides by 4 to eliminate the fraction: $15 + x = 20$ .
Subtract 15 from both sides: $x = 20 - 15$ , so $x = 5$ .

Hence, the number that can be added without changing the average is $x = 5$ .

Therefore, the correct choice from the provided options is option 3:

$5$

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Rule: To maintain average, new number must equal current average
Technique: Set up equation $\frac{15 + x}{4} = 5$ and solve for x
Check: Verify $\frac{5+7+3+5}{4} = \frac{20}{4} = 5$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong sum in the equation
Don't forget to add the existing sum correctly = wrong setup! Students often miscalculate 5+7+3 or set up $\frac{x}{4} = 5$ instead. Always find the current sum first (15), then use $\frac{15 + x}{4} = 5$ .

Practice Quiz

Test your knowledge with interactive questions

Calculate the average of $$ 11 $$ and $$ 7 $$ .

FAQ

Everything you need to know about this question

Why does the new number have to equal the current average?

Think of it this way: if you want to keep the same average, the new number can't pull the average up or down. The only number that doesn't change the balance is the current average itself!

What if I add a number larger than 5?

If you add a number larger than 5 (like 7 or 15), it will pull the average upward. If you add a number smaller than 5 (like 0 or 4), it will pull the average downward.

How do I remember the formula for this type of problem?

Remember: $\text{Average} = \frac{\text{Sum of all numbers}}{\text{Count of numbers}}$
When adding one more number, your new count increases by 1, and your new sum increases by that number!

Can I solve this without setting up an equation?

Yes! Since you want the same average (5), and you're adding one more number, think: "What number makes the total increase match the average increase?" The total needs to go from 15 to 20, so add 5!

What happens if I pick one of the wrong answer choices?

If x = 0: New average = $\frac{15+0}{4} = 3.75$ (too low!)
If x = 4: New average = $\frac{15+4}{4} = 4.75$ (still too low!)
If x = 15: New average = $\frac{15+15}{4} = 7.5$ (way too high!)

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