The cost of dinner for a group of tourist is partly constant and partly varies as the number of tourists present. It costs $740.00 when 20 tourists were pre...
Question 1 Report
The cost of dinner for a group of tourist is partly constant and partly varies as the number of tourists present. It costs $740.00 when 20 tourists were present and $960.00 when the number of tourists increased by 10. Find the cost of the dinner when only 15 tourists were present.
Answer Details
The cost \(C\) is partly constant and partly varies as the number of tourists \(n\), so
\[C=a+bn\]where \(a\) (the constant part) and \(b\) (the rate per tourist) are constants.
When \(n=20\), \(C=740\): \(\;740=a+20b\).
When the number increases by 10, \(n=30\), \(C=960\): \(\;960=a+30b\).
Subtract the first equation from the second:
\[960-740=(a+30b)-(a+20b)\Rightarrow 220=10b\Rightarrow b=22\]Then \(a=740-20(22)=740-440=300\).
So \(C=300+22n\). When \(n=15\):
\[C=300+22(15)=300+330=\$630\]The dinner costs \(\$630.00\) when 15 tourists are present.
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