Solve for Container Distribution: 3x, -8, and 62 Total Across Three Streets

Q: Why do I only need one variable instead of three?

Because the problem gives you relationships between the streets! If Hermione has x containers, then Zigmond automatically has 3x, and High has 3x - 8. One variable controls them all!

Q: What if I get the streets mixed up in my final answer?

Always double-check which number goes with which street! The question asks for Hermione, so your x value (10) is the answer, not the larger numbers.

Q: How can I verify my answer makes sense?

Check the relationships: Is Zigmond 3 times Hermione? 30 = 3(10) ✓ Is High 8 less than Zigmond? 22 = 30 - 8 ✓ Do they sum to 62? 10 + 30 + 22 = 62 ✓

Q: What if my equation doesn't simplify to a whole number?

That's okay! Not all word problems have whole number solutions. Just make sure your arithmetic is correct and that fractions make sense in the context (you can't have 2.5 containers!).

System of Linear Equations with Variable Relationships

On Zigmond street there are 3 times more containers than on Hermione street,

on High street there are 8 containers less than on Zigmond street,

in total in this neighborhood there are 62 containers, how many containers are there on Hermione street?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 How many bins are on Herzl Street?

00:03 Let's mark the number of bins on Herzl Street using the unknown X

00:08 Let's express the number of bins on other streets using X

00:12 Let's build an appropriate equation according to the given data

00:15 The sum of the bins equals 62 according to the given data

00:19 Let's collect terms

00:27 Let's arrange the equation so that only the unknown X is on one side

00:33 Let's isolate X

00:38 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

On Zigmond street there are 3 times more containers than on Hermione street,

on High street there are 8 containers less than on Zigmond street,

in total in this neighborhood there are 62 containers, how many containers are there on Hermione street?

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Set up an equation using the given relationships and the total number of containers.
Step 2: Solve the equation to find the number of containers on Hermione street.
Step 3: Verify the solution by checking if it satisfies all conditions given in the problem.

Step 1: The total number of containers is distributed as follows:

Hermione street: $x$
Zigmond street: $3x$
High street: $3x - 8$

Write the equation for the total number of containers:

$x + 3x + (3x - 8) = 62$

Simplify the equation:

$x + 3x + 3x - 8 = 62$

$7x - 8 = 62$

Add 8 to both sides:

$7x = 70$

Divide both sides by 7 to solve for $x$ :

$x = 10$

Step 2: Verify the solution:

Zigmond street: $3x = 3 \times 10 = 30$
High street: $3x - 8 = 30 - 8 = 22$
Check total: $10 + 30 + 22 = 62$

All conditions are satisfied.

Therefore, the number of containers on Hermione street is 10.

By matching with answer choice 3: $\text{(30, 10, 22)}$ , this choice is consistent.

Final Answer

30, 10, 22

Key Points to Remember

Essential concepts to master this topic

Variable Setup: Define one variable and express others using given relationships
Technique: Combine all expressions: x + 3x + (3x - 8) = 62
Check: Verify all conditions: 10 + 30 + 22 = 62 and 30 = 3(10) ✓

Common Mistakes

Avoid these frequent errors

Setting up variables for each street separately
Don't create three separate variables like h, z, g = confusing system! This makes the problem unnecessarily complex and leads to calculation errors. Always express everything in terms of one variable using the given relationships.

Practice Quiz

Test your knowledge with interactive questions

Solve for x:

$$ 2(4-x)=8 $$

FAQ

Everything you need to know about this question

Why do I only need one variable instead of three?

Because the problem gives you relationships between the streets! If Hermione has x containers, then Zigmond automatically has 3x, and High has 3x - 8. One variable controls them all!

How do I know which street to use as my main variable?

Choose the street that others are compared to! Since Zigmond has 3 times more than Hermione and High is compared to Zigmond, Hermione is the base - use x for Hermione.

What if I get the streets mixed up in my final answer?

Always double-check which number goes with which street! The question asks for Hermione, so your x value (10) is the answer, not the larger numbers.

How can I verify my answer makes sense?

Check the relationships: Is Zigmond 3 times Hermione? 30 = 3(10) ✓ Is High 8 less than Zigmond? 22 = 30 - 8 ✓ Do they sum to 62? 10 + 30 + 22 = 62 ✓

What if my equation doesn't simplify to a whole number?

That's okay! Not all word problems have whole number solutions. Just make sure your arithmetic is correct and that fractions make sense in the context (you can't have 2.5 containers!).

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