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? $\newline$ (Round to the nearest percent. Ignore the $\%$ symbol when entering your answer. For example, if the answer is $11.2 \%$ , enter $11$ .)

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?

\newline

(Round to the nearest percent. Ignore the

\%

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

11.2 \%

, enter

11

Calculate $1$ st Contact Percentage: Calculate the percentage of salespeople who gave up after the $1$ st contact. $\newline$ $44\%$ of salespeople gave up after the $1$ st contact, so $100\% - 44\% = 56\%$ of the salespeople continued to the $2$ nd contact. $\newline$ Calculation: $100 - 44 = 56$
Calculate $2$ nd Contact Percentage: Calculate the percentage of salespeople who gave up after the $2$ nd contact. $\newline$ Of the remaining $56\%$ , $40\%$ gave up after the $2$ nd contact. So, $56\% \times (100\% - 40\%) = 56\% \times 60\%$ of the salespeople continued to the $3$ rd contact. $\newline$ Calculation: $56 \times 0.60 = 33.6$
Calculate $3$ rd Contact Percentage: Calculate the percentage of salespeople who gave up after the $3$ rd contact. $\newline$ Of the remaining $33.6\%$ , $41\%$ gave up after the $3$ rd contact. So, $33.6\% \times (100\% - 41\%) = 33.6\% \times 59\%$ of the salespeople continued to the $4$ th contact. $\newline$ Calculation: $33.6 \times 0.59 = 19.824$
Round Final Percentage: Round the final percentage to the nearest percent. $\newline$ The percentage of salespeople who made $4$ or more contacts is approximately $19.824\%$ , which rounds to $20\%$ when rounded to the nearest percent. $\newline$ Calculation: $\text{Round}(19.824) = 20$