Solving a word problem with three unknowns using a linear equation

Question

Over the last three evenings, Rita received a total of 111 phone calls at the call center. The second evening, she received 9 more calls than the first evening. The third evening, she received 4 times as many calls as the first evening. How many phone calls did she receive each evening?

Number of phone calls the first evening ?

Number of phone calls the second evening?

Number of phone calls the third evening?

Answer 1

Let’s first set up the equations. To do so, we need some variables to denote several unknowns. Say,

the number of phone calls on the 1st day is x

the number of phone calls on the 2nd day is y

the number of phone calls on the 3rd day is z

Here, x, y, z are our variables.When we find the values of these 3 variables, we then have solved this math problem.

How do we set up our equations? By the info provided to us in the problem itself.

there are total 111 phone calls for the 3 days: x + y + z = 111

the number of phone calls on the 2nd day is 9 more than that on the 1st day: y - x = 9

the number of phone calls on the 3rd day is 4 times of 1st day: z = 4x

Putting 3 equations together:

x + y + z = 111

y - x = 9

z = 4x

We have 3 equations 3 unknowns. You now may solve for x, y, z.

Hope this is helpful.