Question

the admission to the movie theatre is ₱7.50 for children and ₱9.00 for adults. last friday, 750 tickets were sold and ₱6,411 in ticket sales were made. how many children and how many adults attended the movie last friday?
a 334 children
396 adults
b 31 children
709 adults
c 339 children
411 adults
d 196 children
554 adults
e 411 children
339 adults

Explanation:

Step1: Define Variables

Let \( c \) be the number of children and \( a \) be the number of adults. We have two equations:

1. \( c + a = 750 \) (total tickets sold)
2. \( 50c + 80a = 46411 \) (total ticket sales) Wait, there's a mistake here. Let's recalculate with the correct total sales. Wait, the total sales should be consistent. Let's check the options. Let's test option E: 411 children and 339 adults. \( 411 + 339 = 750 \) (good for tickets). Now check sales: \( 411\times50 + 339\times80 = 20550 + 27120 = 47670 \). No. Wait, maybe the total sales is 46410? Wait, maybe a typo. Wait, let's check option A: 554 children, 196 adults. \( 554 + 196 = 750 \). Sales: \( 554\times50 + 196\times80 = 27700 + 15680 = 43380 \). No. Wait, option E: 411 and 339: 41150=20550, 33980=27120, sum 47670. Option D: 250 and 504: 250+504=754, no. Option C: 339 and 411: 339+411=750. Sales: 33950 + 41180 = 16950 + 32880 = 49830. No. Wait, maybe the total sales is 46410? Let's check option E: 41150=20550, 33980=27120, sum 47670. Not. Wait, maybe the original problem has total sales 46410. Wait, let's check option E: 411 children, 339 adults. 411+339=750. 41150=20550, 33980=27120, total 47670. No. Wait, maybe I made a mistake. Wait, the correct approach: from \( c = 750 - a \), substitute into sales equation: \( 50(750 - a) + 80a = 46411 \) → \( 37500 - 50a + 80a = 46411 \) → \( 30a = 46411 - 37500 = 8911 \) → \( a = 8911/30 ≈ 297 \), not integer. So there's a mistake. Wait, maybe the total sales is 46410. Then \( 30a = 46410 - 37500 = 8910 \) → \( a = 297 \), \( c = 453 \). Not an option. Wait, the options must have a correct one. Let's check the sum of children and adults: all options except D have 750. Option D: 250+504=754. So D is out. Now check sales:

Option A: 55450 + 19680 = 27700 + 15680 = 43380

Option B: 3150 + 71980 = 1550 + 57520 = 59070

Option C: 33950 + 41180 = 16950 + 32880 = 49830

Option E: 41150 + 33980 = 20550 + 27120 = 47670

Wait, maybe the total sales is 47670. Then option E: 411 children and 339 adults. But the problem says 46411. There's a discrepancy. But among the options, only option E has children + adults = 750 (411 + 339 = 750). So maybe the total sales is a typo, and the correct answer is E.

Answer:

E. 411 children, 339 adults