Q:

A movie theater charges $4.50 for children and $8.00 for adults. On a certain day, 1200 people enter the theater and $8375 is collected. How many children and how many adults attended?

Accepted Solution

A:
Answer:The number of adults who attended=850The number of children who attended=350Step-by-step explanation:a). Determine first expressionLet the number of each group be as follows;adults=achildren=ctotal number of people=1200This can be expressed as;number of people=number of children+number of adultsreplacing;a+c=1200...equation 1b). Determine the second expressionLet the total cost be expressed as shown;total cost=(cost per child×number of children)+(cost per adult×number of adults)where;total cost=$8,375cost per child=$4.5number of children=ccost per adult=$8number of adults=areplacing;(8×a)+(4.5×c)=1,2008 a+4.5 c=8,375...equation 2c). Combine equation 1 and 2 and solve simultaneously1(8 a+4.5 c=8,375)4.5(a+c=1,200)=4.5 a+4.5 c=5,400(8 a-4.5 a)+(4.5 c-4.5 c)=(8,375-5,400)=2,9753.5 a=2,975a=2,975/3.5a=850replacing the value for a in equation 1850+c=1200c=1200-850=350The number of adults who attended=850The number of children who attended=350