Question 1134192: The regular admission rate for a musical is Php 850. For students, senior citizens and persons with disability, the discounted rate is Php 400. The number of tickets sold at the regular rate is 220 less than twice the number sold at the discounted rate. If the total ticket sales is Php 590,000, how many tickets were sold at the discounted rate?
Found 2 solutions by Theo, josgarithmetic:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x equal the number of tickets sold at the regular rate and y equal the number of tickets sold at the discount rate.
the number of tickets sold at the regular rate is 220 less than twice the number sold at the discount rate.
this means that x = 2 * y - 220.
total ticket sales are 590,000 php (philippine pisos).
you have 2 equations that need to be solved simultaneously.
the first equation is x = 2 * y - 220.
the second equation is 850 * x + 400 * y = 590,000 php.
in the second equation, replace x with the equivalent value of 2 * y - 220 from the first equation to get:
850 * x + 400 * y = 590,000 becomes 850 * ((2 * y - 220) + 400 * y = 590,000
simplify to get 1700 * y - 187,000 + 400 * y = 590,000
combine like terms and add 187,000 to both sides of the equation to get:
2100 * y = 777,000
solve for y to get y = 777,000 / 2100 = 370.
since x = 2 * y - 220, this means that x = 520.
520 * 850 + 370 * 400 = 590,000.
the solution checks out ok.
the solution is that 520 tickets were sold at the regular rate and 370 tickets were sold at the discount rate.
Answer by josgarithmetic(39617)  (Show Source):
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