Word Problem x2

Question

If 118 people attend a concert and tickets for adults cost $3.75 while tickets for children cost $2.75 and total receipts for the concert was $365.5, how many of each went to the concert?

Answer 1

Set variables for both the number of adults and number of children.

# adults = X

# children = Y

Set up two equations given the information to solve

.

Number of people:

X + Y = 118 (then solve for Y)

Y=118-X

Cost of tickets:

3.75X+2.75Y= 365.5 (input X from above)

3.75X+2.75(118-X)=365.5

3.75X+324.5-2.75X=365.5

X+324.5=365.5

X = 41

Y=118-41= 77

Answer 2

Number of adult = x

number of children = y

 

 118 people attend a concert

So 

x+ y =118  __________________equation 1

 

total cost for adult = 3.75x

total cost for children = 2.75y

 

total receipts for the concert was $365.5

 

3.75x +2.75y =365.5 ___________equation 2

 

from equation 1 

x+y=118

x=118-y

 

substitute this in equation 2

 

3.75(118-y)+2.75y=365.5

 

442.5 -3.75y +2.75y =365.5

 

442.5 - y =365.5

 

-y = -77

 

y = 77

 

x+ y=118

x+77 =118

x=41

 

Number of adult = x = 41

number of children = y =77