How would you solve this problem?

Question

Suppose that 110 children and 150 adults attend a show for which the total receipts are $1135. If a parent and 4 young children pay $19.00, how much are the adults tickets and how much are the children's tickets?

Answer 1

Assign variables:

    x = cost of adult ticket    [not number of adults]

    y = cost of child ticket     [not number of children]

 

Note:   (cost of one ticket)*(number of people) = dollars

 

Translate:

   "110 children and 150 adults attend"  with "total receipts are $1135"    means

   dollars for children    +    dollars for adults   =    total receipts

         110x                  +           150y             =     $1135             [eq1]

 

   "a parent and 4 young children pay $19.00"   means

          y                     4x              = $19      or

          4x                  +y               = $19              [eq2]

 

Let's use elimination (eliminating y is easy):

     600x     +     150y          =    $2850             [150*eq2]

     110x     +     150y          =    $1135              [eq1]

   -------------------------------------------    [elimination; subtract equations]

     490x                             =     $1715

        x   =   $3.50          [eq3; divide both sides by 490]

 

       4x       +        y            =  $19             [eq2 again]

       4x                               =  $14             [4*eq3]

  -----------------------------------------       [elimination; subtract equations]

                            y           =   $5

 

Check:

    Is    110(3.5) + 150(5) = 1135   ?

            385       +  750   = 1135   ?

                 1135 = 1135   ?yes

    Is    4(3.5) + 5 = 19   ?

                  14  + 5 = 19  ?

                    19 = 19   ?yes

Answer 2

To solve this problem, you would first identify the variables in the problem. 

   x = adults

   y = children

 

With the variables identified you can write the first equation: 

   150x  +  110y   =   1135   ~ this will show how many adult and children tickets were sold to total the amount of receipts

 

To solve the problem you will need the information in the second sentence to create a new equation to help you solve the first equation. 

 

  1x  +  4y  =  19  ~ this represents the one adult ticket and the four children tickets that were sold for $19. Since x is by itself, it would be easier to solve this equation for x. To do this you would need to subtract 4y from each side as shown: 

 

  x  +   4y   =   19

          (-4y)     (-4y)

 

  x              =   19  -  4y

 

 

Since you have solved the equation for x, you can now insert this equation in place of the x in the first equation so all your variable are the same. So the first equation would be rewritten as: 

 

150(19-4y)  +   110y   =   1135  

 

expand this further to read: 

 

(150 * 19)  +  (150 * -4y)   + 110y  = 1135

 

perform the multiplication inside the parentheses:

 

2850 - 600y + 110y  =  1135     ~ after this step, you would then combine the like variables 

 

2850  - 490y  =  1135   ~ since the y value is negative, you can add it to both sides so you are working with a positive variable. You would then subtract 1135 from both sides so that you have the variable isolated on one side. This would be shown as:

 

 2850  -  490y  =  1135

-1135 +  490y  = -1135 + 490y

 1715              =              490y

 

You now have 1715 = 490y    ~ next you would divide each side by 490 to get y by itself

 

1715   =   490y

490     =   490

3.5      =        y

 

From this you can determine that 3.5 = y ~ which is the amount paid for the price of a child ticket. Take this solution and insert it into the second equation of x = 19-4y  ~ This would be shown as:

x  =  19 - (4*3.5)

 

Solve the equation by multiplying 4*3.5 to get 14  ~  this would read x = 19 - 14 ~ finish solving the equation and you will get:   x =  5

 

So the two variables that you solved for

X = 5 (price of adult ticket) and Y = 3.5 (price of child ticket)

 

To verify your work inset the variable amounts into the first equation and solve:

 

150(5)   +   110(3.5)  =  1135

750       +    385        =  1135

     1135     =     1135

 

 

Answer 3

Hi Nick, to solve this problem, use the information given about the parent and four young children. Let A represent the adult and C represent the children.

 

Then:

 

A + 4C = 19

 

Solve for A:

 

A = 19 - 4C

 

Second equation:

 

110C + 150A = 1135

 

Substitute for A:

 

110C + 150 * (19 - 4C) = 1135

 

Clear parenthesis and combine:

 

-490C + 2850 = 1135

 

Subtract 2850 from both sides:

 

-490C = -1715

 

Divide both sides by -490:

 

C = 3.5

 

A child's ticket costs $3.50.

 

Substitute for C in A = 19 - 4C:

 

A = 19 - 14

 

A = 5.00

 

An adult ticket costs $5.00.

 

Check:

 

110 * 3.5 + 150 * 5 = 1135

 

385 + 750 = 1135

 

1135 = 1135

 

Values check.

 

Questions: