23.09.2020

# Shane and abha earned a team badge that required their team to collect no less than 2000 cans for recycling. abha collected 178 more cans than shane did. write an inequality to determine the number of cans, s, that shane could have collected. what is the solution set of the inequality?

47

17.02.2022, solved by verified expert

Shane could have collected more than 911 Cans

Step-by-step explanation:

We are asked to write an inequality to find the number of cans, S that Shane could have collected:

Cans collected by Shane and Abha > 2000

S + A > 2000

Abha collected 178 more cans than Shane did.

A  = 178 + S

Put value of A in the above inequality

S + 178 + S > 2000

2S + 178 > 2000

2S > 2000 - 178

2S > 1822

S > 911

### Faq

Mathematics

Step-by-step explanation:

Let S be the number of cans that Shane had collected.

Abha had collected 178 more cans than Shane did, then Abha had collected S+178 cans.

Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling, this means that

Solve this inequality:

1. Divide it by 2:

2. Now

The solution set is

Mathematics
Mathematics

[911,∞)

Step-by-step explanation:

Given: S be the number of cans collected by Shane.

Since,  Abha collected 178 more cans than Shane did.

Then, the number of cans collected by Abha = S+178

Also, Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.

So,

Hence, the solution set of the inequality will be [911,∞)

Mathematics

[911,∞)

Step-by-step explanation:

Given: S be the number of cans collected by Shane.

Since,  Abha collected 178 more cans than Shane did.

Then, the number of cans collected by Abha = S+178

Also, Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.

So,

Hence, the solution set of the inequality will be [911,∞)

Mathematics

Step-by-step explanation:

Let, the number of cans collected by Shane = x.

So, the number of cans collected by Abha = x + 178.

Since, at least 2000 cans are required to be collected.

Thus, we have the inequality,

Number of cans by Shane + Number of cans by Abha ≥ 2000.

i.e.

i.e.

Thus, the required inequality is .

Mathematics

Inequality is .

Solution set is .

Step-by-step explanation:

Let the number of cans collected by Shane = x and the number of cans collected by Abha = y.

It is given that, Abha collected 178 cans more than Shane.

So, we have, .

Since, they both have to collect cans no less than 2000 i.e. greater than or equal to 2000.

So, the equation representing the situation is,

Shane + Abha ≥ 2000

i.e. y + x ≥ 2000

i.e.

i.e.

i.e.

i.e.

i.e.

Thus, we have,

Inequality for the number of cans Shane collected is .

Solution set of the inequality is .

Mathematics

Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.

This means a minimum of 2000 cans are needed.

Abha collected 178 more cans than Shane did.

Let us suppose that the cans collected by Shane = S

So, Abha collected = S+178

The inequality to determine the cans Shane collected can be given by :

=

Mathematics

Let number of cans collected by Shane =S

Number of cans collected by Abha=S+178

As, it is given that ,Abha collected 178 more cans than Shane did.

Also, the statement about inequality is

Both Shane and Abha have to collect no less than 2000 cans for recycling.

Writing the statement in terms of inequality

S +S+178 ≥ 2000

2 S ≥ 2000 - 178

2 S ≥ 1822

Dividing both sides by 2, we get

S≥ 911

So, Shane must have collected At least 911 cans.

Mathematics

Let number of cans collected by Shane =S

Number of cans collected by Abha=S+178

As, it is given that ,Abha collected 178 more cans than Shane did.

Also, the statement about inequality is

Both Shane and Abha have to collect no less than 2000 cans for recycling.

Writing the statement in terms of inequality

S +S+178 ≥ 2000

2 S ≥ 2000 - 178

2 S ≥ 1822

Dividing both sides by 2, we get

S≥ 911

So, Shane must have collected At least 911 cans.

StudenGPT
Let's solve the problem step by step using mathematical laws and principles.

1. We know that Abha collected 178 more cans than Shane. Therefore, we can represent the number of cans Shane collected as "S."

2. To find the number of cans Abha collected, we add 178 to the number of cans Shane collected, resulting in "S + 178."

3. The task states that the team had to collect no less than 2000 cans, so we can set up an inequality by stating that the combined number of cans collected by Shane and Abha is greater than or equal to 2000:

S + (S + 178) ≥ 2000

4. Now, let’s simplify the inequality. By combining like terms, we have:

2S + 178 ≥ 2000

5. To solve the inequality for S, we subtract 178 from both sides of the inequality:

2S ≥ 2000 - 178
2S ≥ 1822

6. Next, we divide both sides of the inequality by 2 to isolate S:

S ≥ 911

7. Therefore, the inequality that determines the number of cans Shane could have collected is S ≥ 911.

Now let's verify the final answer:

To check if Shane collected at least 911 cans, we substitute S = 911 into the original inequality:

911 + (911 + 178) ≥ 2000
911 + 1089 ≥ 2000
2000 ≥ 2000

Since both sides of the inequality are equal, it confirms that our solution is correct.
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