Question

Over the last three evenings, Martina received a total of 99 phone calls at the call center. The third evening, she received 4 times as many calls as the first evening. The second evening, she received 9 more calls than the first evening. How many phone calls did she receive each evening?

Answer 1

a = number of calls the first evening

b = = number of calls the second evening

c = number of calls the third evening

we know that she received a total of 99 calls, thus whatever "a", "b" and "c" are, we know that a + b + c = 99.

"The third evening, she received 4 times as many calls as the first evening"

c = 4a

"The second evening, she received 9 more calls than the first evening."

b = a + 9


`\bf \begin{cases} a+\underline{b}+\underline{c}=99\\ c=4a\\ b=a+9\\ ----------\\ a+\underline{(a+9)}+\underline{(4a)}=99 \end{cases} \\\\\\ a+a+9+4a=99\implies 6a=99-9\implies 6a=90\implies a=\cfrac{90}{6}`

and surely you know how much that is. Well, she got that many the first night.

how many the second night? well b = a + 9
what about the third night? well, c = 4a.