Adult tickets for a play cost $18 and child tickets cost $10. If there were 24 people at a performance and the theater collected $304 from ticket sales, how many adults and how many children attended the play?
2007-02-23 15:57:59 · 12 answers · asked by nazerbean1 1 in Science & Mathematics ➔ Mathematics
let A = the number of adults
let C = the number of children
304 = A(18) + C(10)
and A + C = 24
so C = 24 - A
substituting into the first equation:
304 = A(18) + (24 - A)(10)
304 = 18A + 240 - 10A
64 = 8A
8 = A
A + C = 24
8 + C = 24
C = 16
2007-02-23 16:07:20 · answer #1 · answered by chem geek 4 · 1⤊ 0⤋
A = number of adult tickets
24 - A = number of child tickets
18A + 10(24 - A) = 304
9A + 5(24-A) = 152 ... divided by 2
9A + 120 - 5A = 152 ... performed the multiplication
4A + 120 = 152 ... performed the subtraction
4A = 32 ... subtracted 120 from both sides
A = 8 ... divided each side by 4
Test:
(8 x 18) + (16 x 10) = 304
144 + 160 = 304
304 = 304
2007-02-23 16:08:56 · answer #2 · answered by Anonymous · 1⤊ 0⤋
18a+10c=304
a+c=24
a= 24-c
18(24-c) +10c=304
432-18c+10c=304
432-8c=304
8c=128
c=16
a+c=24
a + 16 = 24
a= 8
so 8 adult
and 16 children
144 + 160 = 304
2007-02-23 16:10:55 · answer #3 · answered by TALLgirl 3 · 0⤊ 0⤋
let the number of adults be x and number of children be y
x + y = 24 --> x = 24 - y (1)
18x + 10y = 304 (2)
sub (1) into (2)
18(24 - y) + 10y = 304
solve it, therefore y = 16 and x = 8
2007-02-23 16:06:06 · answer #4 · answered by poly grag wondering 1 · 1⤊ 0⤋
a+c=24
10a+10c=240
18a+10c=304
10a+10c=240 subtract
8a=64
a=8
a+c=24
8+c=24
c=16
8 adults & 16 children
check
8*18+10*16=144+160=304
2007-02-23 16:06:04 · answer #5 · answered by yupchagee 7 · 1⤊ 0⤋
a=number of adults
c=number of children
18a+10c=304 and a+c=24
solve for a
a=24-c
so....
18(24-c)+10c=304
432-18c+10c=304
432-8c=304
-8c=304-432
-8c=-128
-8c/(-8)=-128/(-8)
c=16
24-16=8 so a=8
8 adults and 16 children
2007-02-23 16:07:36 · answer #6 · answered by Catman 4 · 1⤊ 0⤋
which means there's a trangle with legs x ( the element you're trying to locate, the area of the bottom of the ladder from the construction) and the wall (it really is 15 ft). Then there's a suitable perspective, and the hypotenuse is 24 ft. (the ladder) so, utilizing pythagorean idea, 15(squared)+x(squared)=24(squared) sparkling up it from there, it is going to probable be extremely straight forward.
2016-12-04 21:08:57 · answer #7 · answered by ? 4 · 0⤊ 0⤋
8 ADULTS AND 16 CHILDREN ATTENDED THE PLAY.
8 X $ 18 = $ 144
16X $ 10 = $ 160
----------------------------
24 = $ 304
----------------------------
2007-02-23 16:18:05 · answer #8 · answered by theprince 1 · 0⤊ 0⤋
A + C = 24
18A+10C=304
Multiply top by -10
-10A-10C=-240
18A+10C=304
----------------------
8A=64
A=8
so children are 24-8 = 16
2007-02-23 16:06:06 · answer #9 · answered by leo 6 · 1⤊ 0⤋
25 kids & 3 adults
ok, obviously I'm not a math person & I see everyone else's answer now, so I guess I'm wrong, but doesn't 25 & 3 also work?
25*10 = 250
18*3 = 54
250 + 54 = 304
Is there more than one right answer?
Oh and now I see how stupid I am - I'm going to stay out of math answers!
2007-02-23 16:02:40 · answer #10 · answered by sweet pea 5 · 0⤊ 1⤋