Mathematical Sentence

[venusaa]

Cinemas sold a total of 2100 movie tickets. Proceeds totaled Php437,500. Tickets can be bought in one of 3 ways: a matinee admission costs Php150, student is Php200 and regular are Php250. How many of each type of ticket was sold if the total tickets of matinee and regular is the same as students’ tickets? how can I translate it into mathematical sentences using the variables m, s and r only.

[bobbinwales]

Long time since night school but will have a go using how would do it on excel formulas150*m +200*s +250*r
Then you can use m+ r =s

[bobbinwales]

First sentence should have ended in = 437500

[bobbinwales]

You allso now m+r+s =2100

[bobbinwales]

So s must be halve of 2100 so 1050

[bobbinwales]

Bobbs worked out the numbers before work so am sure you can now. Will post them if your not able to do it but ask quick as am off soon. You allready know number of Student tickets, s= 1050, and theres definately enough information now to work out Matinee m and Regular r ticket's.
Expect your supposed to do it all with algebra. TBH used a spread sheet myself as have forgot how to work out with algebra but only took a few lines on excel)

[bobbinwales]

Guess you sorted it now venusa? If not will be back at 6 if you want the answer?? Maybe its night time in The Philipenes

[venusaa]

Yes I get it now. Thank you for your answer

[New Judge]

Before you worry about phrasing the question I should have a look at the figures.

Do you mean that if one matinee and one regular ticket is sold then two student tickets are sold? If so then the total tickets sold will be 525 matinee and regular and 1,050 students. These will cost Php420,000. To make the total proceeds Php437,500 you will have to sell 546.875 matinee and regular tickets and 1,093.75 student tickets - a total of 2187.5 tickets. That's if I'm reading the question correctly.

[Prudie]

Mathematically you should do this by simultaneous equations and or substitution, you have 3 unknowns and so need 3 separate equations to solve them. You sentences/equations from the question would be:

150m + 200s + 250r = 437,500
m + r + s = 2,100
m + r = s (easier to solve simultaneously if written as m + r - s = 0)

[jim360]

I disagree with NJ: s = 1050, m = 350, r = 700. I can sort of see where you are coming from, but the reading is that (total matinee + total regular) = total student

[New Judge]

Yes thanks Jim. Can't read questions properly. I blame lockdown :-)