Math word problem help

Question

At the city museum, child admission is
$5.70
and adult admission is
$9.20
. On Wednesday,
155
tickets were sold for a total sales of
$1230.00
. How many adult tickets were sold that day?

Answer 1

This is a common type of problem in algebra and is the intersection of two equations. What I mean is that all the information they give you goes into two equations and you then have to combine them. In this case the two equations are money made and tickets sold. Where total tickets sold is equal to child tickets plus adult tickets. Total money made is money from adults plus children, where money made is tickets sold times cost for either adults or children. Written in equations you'd have

 

T=A+C

-----------------------

T=# of tickets sold

A=# of adult tickets

C=# of child tickets

 

and

$=($_A)+($_C)

----------------------

$=total money

$_A=money from adults

$_C=money from children

(money made needs to be rewritten in terms of tickets so it uses the same variables as the previous equations)

$_A=A*P_A

$_C=C*P_C

----------------------

P_A=Price per adult ticket

P_C=Price per child ticket

 

 

So the two equations we have are

T=A+C

$=A*P_A+C*P_C

 

Now we plug in all the info we have from the question prompt.

PC=5.7

PA=9.2

T=155

$=1230

 

-------------------------

155=A+C

1230=A*(9.2)+C*(5.7)

-------------------------

At this point we need to solve using algebra, specifically solving for one variable and plugging it into the other equation.

C=155-A                                        -Solve for one variable

 

1230=A*(9.2)+(155-A)*(5.7)          -Plug into the other equation

Solve for A and you get

A=99

The number of adult tickets sold is 99

 

What i meant at the beginning by saying were solving for the intersection is this. If you were to graph the two equations

155=A+C
1230=A*(9.2)+C*(5.7)

The answer is the point of intersection between the two. Instead of A and C you can think of them as X and Y.

C=155-A                                                      or  y=155-x
C=(1230-9.2*A)/5.7  =215.789-1.614A         or  y=215.789-1.614X

In the graph below you can see they intersect at (99,56) which is x=99, y=56. In this problem is A=99, C=56.

 

http://www4b.wolframalpha.com/Calculate/MSP/MSP2771gegcee05975f222000021fd64dbd6bh088f?MSPStoreType=image/gif&s=57&w=436.&h=286.&cdf=RangeControl

Answer 2

Let x = the number of adult tickets sold on Wednesday.  Since there were 155 tickets sold in total, the number of child tickets sold was 155-x.

 

Total Sales = (Number of child tickets)*($5.70) + (Number of adult tickets)*($9.20)

 

$1230 = (155-x)($5.70) + (x)($9.20)

 

$1230 = 883.5 - 5.7x + 9.2x

 

346.5 = 3.5x

 

Solve for x.