Question

Over the last three evenings, Maria received a total of 154 phone calls at the call center. The second evening, she received 10 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

Data

• Total phone calls: 154

,

• Second evening ( ,s ,): 10 more calls than the first evening ( ,f ,)

,

• Third evening ( ,t ,): 4 times as many calls as ,f

Procedure

We have to translate the given information into algebraic expressions.

• Maria received a total of 154 phone calls at the call center:

$f+s+t=154$

where f represents the first evening, s the second, and t the third.

• The second evening, she received 10 more calls than the first evening:

$s=10+f$

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

$t=4\times f$

As t and s can be used in terms of f, we will replace the second and third equations that we build in the first one:

$f+s+t=154$$f+(10+f)+(4\times f)=154$

Eliminating the parenthesis we get:

$f+10+f+4f=154$

Solving for f:

$6f=154-10$$f=\frac{144}{6}$$f=24$

Thus, the number of phone calls the first evening was 24.

Then, we have to replace this calculated value in the other equations to get s and t.

• Solving for ,s

$s=10+f$$s=10+24$$s=34$

• Solving for ,t

$t=4f$$t=4\cdot24$$t=96$

To prove our answers are correct, we can do the following:

$24+34+95=154$$154=154$

Answer

• Number of phone calls the first evening: 24

• Number of phone calls the second evening: 34

• Number of phone calls the third evening: 96