Answer:
The inequality required is: \(75 + 4t \geq 400\)
and 82 tickets must be sold to pay for this year's dance.
Step-by-step explanation:
Let t represents the number of tickets sold.
Given: Each ticket to the dance costs is $ 4 and the student treasure reported that the dance fund has $ 75 left over from last year.
Since, each ticket to the dance sold is $4,
therefore the total cost to the dance is 4t
Together with the $75 left carry over,
then we have; 75 + 4t
As per the given conditions :
They must make at least $400 to pay for the dance i.e it must be more than or equal to 400;
which gives you the inequality: \(75 + 4t \geq 400\) where t is the number of tickets sold.
Now, solve this inequality which gives you how many tickets must be sold to pay for this year's dance.
\(75 + 4t \geq 400\)
Subtraction property of equality states that you subtract the same number to both sides of an equation.
Subtract 75 to both sides of an equation;
\(75 + 4t -75 \geq 400-75\)
Simplify:
\(4t\geq 325\)
Division property of equality states that you divide the same number to both sides of an equation.
divide by 4 to both sides of an equation;
\(\frac{4t}{4} \geq \frac{325}{4}\)
Simplify:
\(t\geq 81.25\)
Since, you cannot sell quarter of ticket ;
so, 81.25 rounded up to 82
therefore, 82 tickets must be sold to pay for this year's dance.
