An organization determined most of its sales only occurred after at least $4$ contacts. However, $44\%$ of its salespeople gave up on a customer after the $1^{\text{st}}$ contact didn't make a sale. Of the remaining salespeople, $40\%$ gave up after the $2^{\text{nd}}$ contact. Finally, $41\%$ of the salespeople who made a $3^{\text{rd}}$ contact gave up when that call did not make a sale. To the nearest percent, what percent of the original salespeople made $4$ or more contacts if the first $3$ contacts did not result in sales? (Round to the nearest percent. Ignore the $\%$ symbol when entering your answer. For example, if the answer is $44\%$ $0$ , enter $44\%$ $1$ .)

Full solution

Q. An organization determined most of its sales only occurred after at least

4

contacts. However,

44\%

of its salespeople gave up on a customer after the

1^{\text{st}}

contact didn't make a sale. Of the remaining salespeople,

40\%

gave up after the

2^{\text{nd}}

contact. Finally,

41\%

of the salespeople who made a

3^{\text{rd}}

contact gave up when that call did not make a sale. To the nearest percent, what percent of the original salespeople made

4

or more contacts if the first

3

contacts did not result in sales? (Round to the nearest percent. Ignore the

\%

symbol when entering your answer. For example, if the answer is

44\%

0

, enter

44\%

1

Calculate First Contact Remaining: Determine the percentage of salespeople remaining after the first contact. $\newline$ $44\%$ of salespeople gave up after the first contact, so $100\% - 44\% = 56\%$ of salespeople continued to the second contact.
Calculate Second Contact Remaining: Determine the percentage of salespeople remaining after the second contact. Of the $56\%$ who continued, $40\%$ gave up after the second contact. So, $60\%$ of the remaining $56\%$ continued to the third contact. Calculation: $56\% \times 60\% = 0.56 \times 0.60 = 0.336$ or $33.6\%$ .
Calculate Third Contact Remaining: Determine the percentage of salespeople remaining after the third contact. Of the $33.6\%$ who continued, $41\%$ gave up after the third contact. So, $59\%$ of the remaining $33.6\%$ continued to the fourth contact. Calculation: $33.6\% \times 59\% = 0.336 \times 0.59 = 0.19824$ or $19.824\%$ .
Round Final Percentage: Round the final percentage to the nearest whole number. $19.824\%$ rounds to $20\%$ when rounded to the nearest percent.