Question

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?

Answer 1

Answer: [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, $S+178+S\geq2000$

$\\\Rightarrow\ 2S\geq2000-178\\\Rightarrow2S\geq1822\\\Rightarrow\ S\geq911$

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

Answer 2

The solution set of the inequality is [911,$\infty$) and this can be determined by forming the inequality and simplifying that inequality by using the arithmetic operations.

Given :

• 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.
• The number of cans, S, that Shane could have collected.

The inequality to determine the number of cans, S, that Shane could have collected is given by:

$\rm S + 178 + S \geq 2000$

Now, simplify the above expression by using the following steps:

Step 1 - Addition of S and S in the above expression.

$\rm 2S + 178 \geq 2000$

Step 2 - Subtract 178 from both sides in the above expression.

$\rm 2S +178-178 \geq 2000-178$

$\rm 2S \geq 1822$

Step 3 - Divide both sides by 2.

$\rm S \geq 911$

Hence the solution set of the inequality is [911,$\infty$).

For more information, refer to the link given below:

https://brainly.com/question/25140435