First let's calculate the number of students who will buy lunch 5 times next week and it is given by:-
![\begin{gathered} (35)/(100)*500 \\ =35*5 \\ =175 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/65r9fl1qylav2p4s1na4iz90sqcrnqz8ue.png)
So 175 students will buy lunch 5 times.
Similarly let's find number of students who will buy lunch 4 times
![\begin{gathered} (15)/(100)*500 \\ =15*5 \\ =75 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/hhuyocplbceo6dggqb7ky4ne6n715d5fc1.png)
75 students will buy 4 times
Similarly on calculation we get 50 students will buy 3 times, 50 students will buy 2 times , 90 students will buy 1 time.
So total number of lunches that will be sold will be
![\begin{gathered} 5*175+4*75+3*50+2*50+1*90 \\ =875+300+150+100+90 \\ =1515 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/30j2zuwd81ycj92szgahiq822aupwq8v1f.png)
So total 1,515 lunches will be sold .Hence the correct option is (A).