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Sagot :
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:
[tex]f+s+t=154[/tex]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:
[tex]s=10+f[/tex]• The third evening, she received 4 times as many calls as the first evening:
[tex]t=4\times f[/tex]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:
[tex]f+s+t=154[/tex][tex]f+(10+f)+(4\times f)=154[/tex]Eliminating the parenthesis we get:
[tex]f+10+f+4f=154[/tex]Solving for f:
[tex]6f=154-10[/tex][tex]f=\frac{144}{6}[/tex][tex]f=24[/tex]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
[tex]s=10+f[/tex][tex]s=10+24[/tex][tex]s=34[/tex]• Solving for ,t
[tex]t=4f[/tex][tex]t=4\cdot24[/tex][tex]t=96[/tex]To prove our answers are correct, we can do the following:
[tex]24+34+95=154[/tex][tex]154=154[/tex]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
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