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Mrs. Morton has a special reward system for her class. When all her students behave well, she rewards them by putting 3 marbles into a marble jar. When the jar has 100 marbles or more, the class has a party. Right now, the jar contains 24 marbles.
Let r represent the number of additional times the class is rewarded. Write an inequality to determine how many more times the class needs to be rewarded in order to earn a party.

What is the minimum whole number of additional times they need to be rewarded so they can have a party?

Respuesta :

JeanaShupp

Answer: [tex]24+3r\geq100[/tex]

r=26


Step-by-step explanation:

Given: Mrs. Morton rewards her students on behave well by putting 3 marbles into a marble jar.

If the jar contains 24 marbles. and r represent the number of additional times the class is rewarded then the required equation will be

[tex]24+3r\geq100[/tex]

If we solve it, we will get the minimum the jar contains 24 marbles.

To solve equation, subtract 24 from both sides, we get

[tex]3r\geq100-24\\\Rightarrow3r\geq76\\\Rightarrow\ r\geq\frac{76}{3}\geq25.333\approx 26[/tex]

Hence, the minimum whole number of additional times they need to be rewarded so they can have a party=26

To solve the problem we must know about Expressions.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The class needs to behave well 26 times to get a party.

Given to us

  • Mrs. Morton rewards them by putting 3 marbles into a marble jar.
  • When the jar has 100 marbles or more,
  • Right now, the jar contains 24 marbles.

Assumption

Assume that the number of times they behave well is x.

Expression to state the number of marbles in the jar,

As we know the jar already had 24 marbles and the number of marbles they get each time they behave well is 3, therefore, the expression can be written as,

24 + 3x

Also, the jar must have marbles equal to more than 100,

100 ≤ 24 + 3x

Thus, the expression for the jar can be written as 100 ≤ 24 + 3x.

Minimum number of times students need to behave well

To get the minimum number of times they must behave well solve the expression above for x,

100 ≤ 24 + 3x

To get the minimum value we will solve it for 100 = 24+3x,

[tex]100=24+3x\\100-24 = 3x\\76= 3x\\\\x = \dfrac{76}{3}\\\\x = 25.3334[/tex]

we need a whole number but 25 won't fulfill the condition, therefore, the number of times they need to behave well is 26.

Hence, the class needs to behave well 26 times to get a party.

Learn more about Expressions:

https://brainly.com/question/13947055

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