Question

The Homecoming committee wants to raise between $1500 and $2000 at the dance.They have already saved $800 to put towards the dance. If tickets are $20 each, howmany tickets must they sell? Variable Represents:Inequality:Solve:Sentence:

Answer 1

35≤t≤60

Step-by-step explanation:

Let the variable t represents the number of tickets they must sell.

Cost of a ticket =$20

• Cost of t tickets =$20t

Since they have already saved $800

Total balance = 800+20t

The committee wants to raise between $1500 and $2000 at the dance.

Therefore, the inequality representing this situation is:

`1500\leqslant800+20t\leqslant2000`

We solve for t.

`\begin{gathered} 1500\leqslant800+20t\leqslant2000\text{ (Subtract 800 from all sides)} \\ 1500-800\leqslant800-800+20t\leqslant2000-800 \\ 700\leqslant20t\leqslant1200\text{ (Divide all through by 20)} \\ (700)/(20)\leqslant(20t)/(20)\leqslant(1200)/(20) \\ 35\leqslant t\leqslant60 \end{gathered}`

The homecoming committee must sell between 35 and 60 tickets to meet their goal.