Question

Solve the problem. Chapter 12.4 The Little Town Fine Arts Center charges $24 per adult and $11 per senior citizen for its performances. On a recent weekend evening when 516 people paid admission, the total receipts were $7431. How many who paid were senior citizens? RESPOND TO EACH OF THE FOLLOWING STATEMENTS BE SURE TO PROPERLY LABEL RESPONSES WITH THE APPROPRIATE LETTER A) What sequation can be written for the number of tickets sold B) What equation can be written for the money taken in for ticket sales C) How many adult tickets were sold D) How many senior tickets were sold

Answer 1

Let number of adult ticket is x and number of senior citizens ticket is y .

A) total number of ticket is 516 . So equation for number of ticket is

x+y= 516

B) cost for x adult ticket is 24x .

cost for y senior ticket is 11y .

total cost is sum of this two cost and equal to 7431 .so equation for this is

24x+11y= 7431

c) on rearranging ticket equation

y=516-x

apply this value of y into second equation

24x+11(516-x)= 7431

simplify and find value of x

24x+5676-11x= 7431

13x= 7431-5676=1755

x=1755/13=135

so number of adult ticket = x= 135

d)

number of senior citizens ticket= y= 516-x = 381

there are 381 senior