Question

Traci collects donations for a dance marathon. One group of sponsors will donate a total of $6for each hour she dances. Another group of sponsors will donate $75 no matter how long shedances.14. Write an inequality to show how long she will need to dance to make at least $500.A. 6H+75H=500B. 6H+75>500C. 6H-75<500At D. 75H +6>500what number of hours should Traci dance if she wants to raise at Atleast $500?

Answer 1

Let's call H the number of hours she dances. So, one group of sponsors will donate a total, in dollars:

`6H`

Also, the other group of sponsors will donate a total, in dollars:

`75`

So, she will make:

`6H+75`

For that value to be at least $500, we have:

`6H+75\ge500`

Now, we can find the number of hours Trace should dance if she wants to raise at least $500 by solving the above inequality.

We obtain:

`\begin{gathered} 6H+75\ge500 \\ \\ 6H\ge500-75 \\ \\ 6H\ge425 \\ \\ H\ge(425)/(6) \\ \\ H\ge70.83 \end{gathered}`

Therefore, she should dance for at least 70.83 hours. Rounding to the nearest integer hour, we can say she should dance for at least 71 hours.