word problem involving ratios

[lucasm1]

If 30% of ticket holders pay $4 for a childrens ticket and the rest pay 8.50 for adult tickets. The total amt spent on childrens tickets was $252 ,what was the total tickets sold for both childrens and adult?

 

[tkhunny]

If 30% of ticket holders pay $4 for a childrens ticket and the rest pay 8.50 for adult tickets. The total amt spent on childrens tickets was $252 ,what was the total tickets sold for both childrens and adult?

Set it up in a rational order.

C = Price of Child's Ticket = 4.00
A = Price of Adult's Ticket = 8.50

c = Number of Child Ticket Holders
a = Number of Adult Ticket Holders

"what was the total tickets sold for both children and adult?"

a + c = Total Tickets Sold
a*A + c*C = Total Ticket Sales

Now, what do we know?

30% are children ==> c/(a+c) = 0.30 ==> c = 0.30*(a+c) ==> 0.30*a = c-0.30c = 0.70*c ==> a = (.7/.3)*c = (7/3)*c

$252 spend on kids ==> C*c = 252

C = Price of Child's Ticket = 4.00 ==> 4.00*c = 252 ==> c = 63 -- I'm glad this is Integer.

a = (7/3)*c = (7/3)*63 = 147

a*A + c*C = Total Ticket Sales
(147)*(8.50) + (63)*(4.00) = Total Ticket Sales = ??

63/(147+63) = 63/210 = 0.30 -- Perfect.
c*C = 63*4.00 = 252.00 -- Perfect.

This one takes a little oganization.

 

[lucasm1]

This problem is for a 5th grader. How would she set it up as a simple ratio?

Thank you for your answer

 

[Denis]

Given: 252 / 4 = 63 kid tickets.

If 30% = 63, then 70% = 63/30 * 70 = 147 = adult tickets
Is that what you mean by "ratio"?

Notice that the $8.50 as adult ticket cost is irrelevant,
since the number of tickets is what's asked for.

 

[tkhunny]

This problem is for a 5th grader. How would she set it up as a simple ratio?

Thank you for your answer

Well, that's the way I would have done it in 5th grade...not really. You really do need to provide useful information up front.

 

[lucasm1]

Thanks again