Adult tickets for a play cost $15 and child tickets cost $13. If there were 20 people at a performance and the theater collected $294 from ticket sales, how many children attended the play?
2007-09-16 03:31:37 · 8 answers · asked by tbond_1969 1 in Science & Mathematics ➔ Mathematics
c = # of children
a = # of adults
20 people at a performance
1) c + a = 20
a = 20 - c
the theater collected $294 from ticket sales
2) 15a + 13c = 294
15(20 - c) + 13c = 294 {substitute from equation 1}
300 - 15c + 13c = 294
- 2c = - 6
c = 3
a = 20 - 3 = 17
Check
15(17) + 13(3) = 294
255 + 39 = 294
294 = 294
2007-09-16 03:40:40 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Substitution Method
Let
c = Children
a = Adults
20 = total children and adults
13c = cost of the child ticket
15a = cost of the adult ticket
294 = total collected
- - - - -
c + a = 20- - - - - - - - - Equation 1
13x + 15a = 294- - - - Equation 2
- - - - - - - - - - - --
Isolate the a variable in equation 1
c + a = 20
c + a - c = - c + 20
a = - c + 20
Substitute the a value into equation 2
- - - - - - - - -
13c + 15a = 294
13c + 15( - c + 20) = 294
13c +( - 15c + 300) = 294
Remove parenthesis
13c - 15c + 300 = 294
Colllect like terms
- 2c + 300 = 294
Transpose 300
- 2c + 300 - 300 = 294 - 300
Collect like terms
- 2c = - 6
Divide both sides of the equation by - 2
- 2c / - 2 = - 6 / - 2
c = - 6 / - 2
c = 3. . .←. .Number of children
Insert the c value into equation 1
- - - - - - -
c + a = 20
3 + a = 20
Transpose 3
3 + a - 3 = 20 - 3
Collect like terms
a = 17
Insert the a value into equation 1
- - - - - - - - -
Check for equation 1
c + a = 20
3 + 17 = 20
20 = 20
- - - - - - - -
Check for equation 2
13c + 15a = 294
13(3) + 15(17) = 294
39 + 255 + 294
294 = 294
- - - - - - - - - -
Both equations balance
3 children attended the play
- - - - - - -s-
2007-09-16 04:23:52 · answer #2 · answered by SAMUEL D 7 · 0⤊ 0⤋
number od adults = x
number of children = y
x+y=20 -- (1)
15x+13y=294 -- (2)
from (1) y=20-x
(2) becomes, 15x+13(20-x)=294
15x+260-13x=294
2x+260=294
2x=294-260=34
x=17 (number of adults)
y= 3 (number of children)
check: 17($15)+3($13)=255+39=294
2007-09-16 04:13:48 · answer #3 · answered by cidyah 7 · 0⤊ 0⤋
The answers 3.
Solution:
Let x and y be no of adults and children respectively. Then
15x + 13 y = 294
(-)(13x+13y = 260) i.e. 13(x+y = 20)
--------------------------
2x= 34
=> x = 17
=> y = 3
2007-09-16 03:46:06 · answer #4 · answered by tom 1 · 0⤊ 0⤋
Let's say there were c children at the performance.
That means there were 20-c adults.
The income from children's tickets was 13c.
The income from adult tickets 15(20-c)=300 - 15c
The income for the whole performance was
13c + 300 - 15c = 294
You should be able to take it from here.
2007-09-16 03:51:29 · answer #5 · answered by gugliamo00 7 · 0⤊ 0⤋
i'm maths instructor sending you this counsel: a million) do no longer restoration unique time, 2) activity is the motivating element to be taught arithmetic. 3) very maximum crucial factor to be suggested is "prepare Examples and workouts in basic terms. 4) do no longer bypass over any financial disaster. 5) while you're a scholar of state board,do no longer be taught something from out area the text textile e book. 6) Refer previous twelve months questions. 6) if ISC, you will desire to refer extra books. 7) activity and frustrating artwork with useful might carry you 100percentsuccesses
2017-01-02 06:42:15 · answer #6 · answered by ? 3 · 0⤊ 0⤋
15(x)+13(20-x)=294
15x+260-13x=294
2x+260=294
2x=34
x=17
20-17=3
3 children attended play
2007-09-16 03:47:07 · answer #7 · answered by Prayingmantis 1 · 0⤊ 0⤋
3 children.
I think.
2007-09-16 03:42:51 · answer #8 · answered by Anonymous · 0⤊ 0⤋