Layla and Nathan each sent out college recruitment e-mails to different prospective students. Students followed a link to get more information from $22 \%$ of Layla's $400$ e-mails and from $60$ out of $350$ of Nathan's e-mails. To the nearest percent, what percent of the total students clicked on the link from the e-mails? $\newline$ (Ignore the $\%$ symbol when entering your answer. For example, if the answer is $12 \%$ , enter $12$ .)

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Find what percent one number is of another: word problems

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Q. Layla and Nathan each sent out college recruitment e-mails to different prospective students. Students followed a link to get more information from

22 \%

of Layla's

400

e-mails and from

60

out of

350

of Nathan's e-mails. To the nearest percent, what percent of the total students clicked on the link from the e-mails?

\newline

(Ignore the

\%

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

12 \%

, enter

12

Calculate students from Layla's emails: Calculate the number of students who followed the link from Layla's e-mails. $\newline$ Layla's response rate is $22\%$ , and she sent out $400$ e-mails. $\newline$ To find the number of students who clicked on the link, we multiply the total number of e-mails by the response rate. $\newline$ Number of students from Layla's e-mails = $22\%$ of $400$ $\newline$ Number of students from Layla's e-mails = $0.22 \times 400$ $\newline$ Number of students from Layla's e-mails = $88$
Calculate students from Nathan's emails: Calculate the number of students who followed the link from Nathan's e-mails. $\newline$ We are given that $60$ out of $350$ of Nathan's e-mails were followed by students. $\newline$ Number of students from Nathan's e-mails = $60$
Calculate total students from both emails: Calculate the total number of students who clicked on the links from both Layla's and Nathan's e-mails. $\newline$ Total number of students who clicked on the links $=$ Number of students from Layla's e-mails $+$ Number of students from Nathan's e-mails $\newline$ Total number of students who clicked on the links $= 88 + 60$ $\newline$ Total number of students who clicked on the links $= 148$
Calculate total emails sent: Calculate the total number of e-mails sent by both Layla and Nathan. $\newline$ Total number of e-mails sent = Layla's e-mails + Nathan's e-mails $\newline$ Total number of e-mails sent = $400 + 350$ $\newline$ Total number of e-mails sent = $750$
Calculate overall response rate: Calculate the overall response rate to the nearest percent. $\newline$ Overall response rate = $(\frac{\text{Total number of students who clicked on the links}}{\text{Total number of e-mails sent}}) \times 100\%$ $\newline$ Overall response rate = $(\frac{148}{750}) \times 100\%$ $\newline$ Overall response rate \approx $19$ . $73$ \% $\newline$ To the nearest percent, the overall response response rate is approximately $20\%$ .