Question

the sophomores class is planning a pienic .the cost of the permit the use a city park is $250 .to pay for the permit .there is few of $.75for each sophomore and for each guest who is not a sophomore .two hundred sophomore plan to attend write and solve an inequality to find how many guests must attend for sophomore to pay for permit

Answer 1

200 sophomores will attend the picnic.

Since each of them will pay $0.75, the amount gathered by the 200 sophomores is:

`0.75*200=150`

They have $150 and they need $250 for the permit to use the city park.

Thus, the amount they need to gather from the guest is:

`250-150=100`

To pay for the permit, the amount from the guest has to be equal to or greater than 100.

This inequality can be represented as 0.75x, where x is the number of guests, and that has to be greater than 100 because 0.75x is the amount they will gather from the guests.

The inequality is as follows:

`0.75x\ge100`

And now we solve this inequality for x by dividing both sides by 0.75:

`\begin{gathered} (0.75x)/(0.75)\ge(100)/(0.75) \\ x\ge133.33 \end{gathered}`

133.33 guests must attend. Since we are talking about people, we need to round this number up to 134 people.

Answer:

134 guests