Question

Mrs. Morton has a special reward system for her class when all her students behave well she rewards them by putting three marbles into a marble jar. When the jar is 100 or more marbles the students have a party. Right now the jar has 24 marbles. Write an inequality to determine the number of additional times Mrs. Morgan could reward the class in order for the students to have a party. Will the students have a party if Mrs. Morton rewards them 31 additional times? Choose one answer.

Answer 1

`\begin{gathered} 3x+24\ge100 \\ \\ \text{ Yes} \end{gathered}`

Step-by-step explanation

Let the number of additional times be x.

Every time the students are well behaved, Mrs.Morton puts 3 marbles into the jar. This implies that if they behave x more times, she will put 3x marbles into the jar.

Right now there are already 24 marbles in the jar, so the total number of marbles after x additional times will be:

`3x+24`

There must be 100 or more marbles in the jar in order for them to have a party. This implies that the inequality that represents the number of additional times that Mrs. Morton could reward them is:

`3x+24\ge100`

That is the inequality.

Let us now solve the inequality to find the number of times:

`\begin{gathered} 3x+24\ge100 \\ \\ 3x\ge100-24 \\ \\ 3x\ge76 \\ \\ x\ge(76)/(3) \\ \\ x\ge25.33 \end{gathered}`

Since the number of additional times must be an integer, then, Mrs. Morton must reward them 26 more times for them to be able to have a party.

Since 31 is greater than 26, then, the students will have a party if Mrs. Morton rewards them 31 additional times.

The answer is Yes.