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Pine Bluff Middle School is having its annual Spring Fling dance, which will cost \$400$400dollar sign, 400. The student treasurer reported that the dance fund has \$75$75dollar sign, 75 left over from last year. Each ticket to the dance costs \$4$4dollar sign, 4. Let ttt represent the number of tickets sold. Write an inequality to determine how many tickets must be sold to pay for this year's dance. What is the minimum whole number of tickets that must be sold to fund the dance?

Verified Answer :

calculista

Let

t---------> represent the number of tickets sold

Part a) Write an inequality to determine how many tickets must be sold to pay for this year's dance

we know that

\(4t+75 \geq 400\\ 4t \geq (400-75)\\ 4t \geq 325\\ t \geq 325/4\\ t \geq 81.25\)

therefore

the answer Part a) is

The inequality to determine how many tickets must be sold to pay for this year's dance is equal to \(t \geq 81.25\)

Part b) What is the minimum whole number of tickets that must be sold to fund the dance?

if

\(t \geq 81.25\)

then

the minimum whole number is \(82\)

therefore

the answer Part b) is

\(82\)

The correct answers are:

The inequality is 75+4t ≥ 400, and they must sell at least 82 tickets.

Explanation:

t is the number of tickets sold. They start out with $75, so that is where our inequality begins. Each ticket is $4; this gives us the expression 4t. Together with the $75 carry over, we have 75+4t.

They must make at least $400 to pay for the dance. This means it must be more than or equal to 400; this gives us 75+4t ≥ 400.

To solve this, first subtract 75 from each side:

75+4t-75 ≥ 400-75

4t ≥ 325

Divide both sides by 4:

4t/4 ≥ 325/4

t ≥ 81.25

We cannot sell a portion of a ticket, so we round. While mathematically this number would "round down," if they only sell 81 tickets, they will not have enough money. Therefore we round up to 82.

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