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

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?

Video Solution

Solution Steps

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 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:

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:

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.