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Question

Write an equation to model each situation. Then solve.

 

The attendance at a baseball game was 400 people. Student tickets cost $2 and adult tickets cost $3. Total ticket sales were $1050. How many tickets of each type were sold?

 

The perimeter of a pool table is 30 ft. The table is twice as long as it is wide. What is the length of the pool table?

Answer 1

Let x be the number of $2 tickets and let y be the number of $3 tickets,  Then one can write two equations:

 

x + y =  400                                the total number of tickets sold, and

 

2x + 3y = 1050                            the amount of money from the ticket sales

 

Solve the first equation for x:  x = 400 - y,  and place this value for x into the second equation:

 

 

2(400 - y) + 3y = 1050, multiply through:  800 -2y + 3y = 1050, gather like terms and subtract 800 from both sides of the equation, this yields  y = 250.

 

Place this value into the first equation,  x + 250 = 400 and solve for x by subtracting 250 from both sides of the equation, this yields x = 150.  

 

Therefore, 150 $2 tickets and 250 $3 tickets were sold.  

 

 

 

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Let x be the width and 2x be the length, remembering that a rectangular pool table has four sides, one can write:

 

x + 2x + x + 2x  = 30, gather up the x terms:  6x = 20 and divide both sides by 6, yielding x = 5 ft, the width and 2x = 10 ft, the length.  

Answer 2

let x be the number of student tickets

let y be the number of adult tickets

 

so,

 

x + y = 400  ----------> x = 400 - y

 

2x + 3y = 1050

 

2(400 - y) + 3y = 1050

 

800 - 2y + 3y = 1050

 

y = 1050 - 800 = 250

 

so x = 400 - 250 = 150

 

x = 150, y = 250

 

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perimeter: 30ft

 

let l be length

let w be width

 

l =2w

 

so,

 

2(2w) + 2w = 30

 

6w = 30

 

w = 5

 

so, l = 10 ft.