SOLUTION: Over the last 3 evenings, Latoya received a total of
77 phone calls at the call center. The third evening, she received
5 fewer calls than the first evening. The second evening
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77 phone calls at the call center. The third evening, she received
5 fewer calls than the first evening. The second evening
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Question 1079944: Over the last 3 evenings, Latoya received a total of
77 phone calls at the call center. The third evening, she received
5 fewer calls than the first evening. The second evening, she received
2 times as many calls as the third evening. How many phone calls did she receive each evening?
You can put this solution on YOUR website! first evening is x
third evening is x-5
the second evening is 2(x-5)=2x-10
They add to 77
x+x-5+2x-10=77
4x-15=77
4x=92
x=23 first evening
2x-10=36 second evening
x-5=18 third evening
let x = the number of calls she received the first evening
let y = the number of calls she received the second evening.
let z = the number of calls she received the third evening.
x + y + z = 77
the third evening she received 5 fewer calls than the first evening.
z = x - 5
the second evening she received 2 times as many call as as the third evening.
y = 2z
you have the following 3 equations that need to be solved simultaneously,
x + y + z = 77
z = x - 5
y = 2z
you want to eliminate 2 of the variables in the first equation so you can solve for the third.
replace z with x - 5 in the first equation to get:
x + y + x - 5 = 77
combine like terms to get:
2x + y - 5 = 77
in the equation of y = 2z, replace z with x - 5 to get:
y = 2 * (x - 5)
simplify to get y = 2x - 10
in the equation of 2x + y - 5 = 77, replace y with 2x - 10 to get:
2x + 2x - 10 - 5 = 77
combine like terms to get:
4x - 15 = 77
add 15 to both sides of the equation to get:
4x = 92
divide both sides of the equation by 4 to get:
x = 23
you started with:
x + y + z = 77
z = x - 5
y = 2z
since x = 23, these equations became:
24 + y + z = 77
z = 23 - 5 = 18
y = 2z = 2 * 18 = 36
you have:
x = 23
y = 36
z = 18
x + y + z becomes 23 + 36 + 18 = 77
z = x - 5 becomes z = 23 - 5 = 18
y = 2z becomes y = 2 * 18 = 36
