Question

A total of 70 tickets were sold for a concert and earn the organizers $804. If the cost of each ticket is either $10 or $12, how many tickets of each type were sold?

Answer 1

X=18

Y=52

Explanation:

Let X represent the first type of ticket sold at the concert

Let Y represent the second type of ticket sold at the concert-----equation 1

X + Y= 70 (Total number of tickets sold) ------equation 2

(X×10) + ( Y×12)=$804. ( Total money generated in the concert

Since,

X+Y= 70

X= 70-Y

Substitute (70-Y) for X in equation 2

(70-Y)×10 + Y×12=804

700-10Y+12Y= 804

Collect the like terms

700+2Y=804

2Y=804-700

2Y= 104

Divide both sides by the coefficient of Y which is 2

2Y/2= 104/2

Y=52

Substitute 52 for Y in equation 1

X+Y=70

X+ 52=70

collect the like terms

X= 70-52

X=18

Hence the first type of ticket sold is 18 tickets and the second type of ticket sold is 52 tickets.