Question

Chase and his brother want to improve their personal information for when they startapplying to colleges of their choice. To accomplish this they decide to help the SalvationArmy with delivering hot meals to senior citizens. About a month ago, they decided tokeep track of how many successful deliveries they have each completed. As of today,Chase has successfully delivered 18 out of the 30 meals to senior citizens.Part AHow many more meals would Chase have to deliver in a row in order to have a 75%successful delivery record? Justify your answer.Part BHow many more meals would Chase have to deliver in a row in order to have a 90%successful delivery record? Justify your answer.PartAfter successfully delivering 18 out of 30 meals would Chase ever be able to reach a100% successful delivery record? Explain why or why not.

Answer 1

Part A.

Chase has successfully delivered 18 out of the 30 meals to senior citizens.

We have to calculate how many more meals (lets call it x) she has to deliver to have a 75% successful delivery record.

In order to do that, (18+x) meals have te be delivered successfully out of (30+x), and the successful meals (18+x) divided by (30+x) has to be 0.75:

`\begin{gathered} (18+x)/(30+x)=0.75 \\ 18+x=0.75(30+x) \\ 18+x=22.5+0.75x \\ x-0.75x=22.5-18 \\ 0.25x=4.5 \\ x=(4.5)/(0.25) \\ x=18 \end{gathered}`

Chase has to deliver 18 more meals successfully in order to have a 75% success delivery record.

Part B.

We apply the same analysis but we replace 0.75 with 0.9 as the delivery record.

`\begin{gathered} (18+x)/(30+x)=0.9 \\ 18+x=0.9(30+x) \\ 18+x=27+0.9x \\ (1-0.9)x=27-18 \\ 0.1x=9 \\ x=(9)/(0.1) \\ x=90 \end{gathered}`

Chase has to deliver 90 more meals successfully in order to have a 90% success delivery record.

Part C.

She won't be able to achieve 100% successful delivery record. We can prove it mathematically, but we already know as there are 12 meals that weren't successfully delivered, so we can get close to 100% but it can't never be reached.

Mathematically we have:

`\begin{gathered} (18+x)/(30+x)=1 \\ 18+x=30+x \\ x-x=30-18 \\ 0=12 \end{gathered}`

This solution is not valid, so there is no valid solution for x.