word problems? help?

Question

Adult tickets for a play cost $13 and child tickets cost $11. If there were 23 people at a performance and the theater collected $263 from ticket sales, how many children attended the play?
A) 17 children
B) 18 children
C) 19 children
D) 5 children


The sum of two numbers is 70. The second is 1 more than 2 times the first. What are the two numbers?


One number is 12 more than another. The sum of the smaller number and twice the larger number is 39. Find the larger number.
A) 5
B) 7
C) 17
D) 34

Given f(x) = 5x2 – 3x + 1, find f(–2).
A) –13
B) 15
C) –25
D) 27

Given f(x) = –4x + 5, find f(–4).

Answer 1

let a be the adult's ticket
let c be the children's tickets

There were 23 people attended the performance including both adult and childred.
a + c = 23

adult ticket cost $13 and children tickets cost $11. THe total is $263

13a + 11c = 263

a = 23 - c

13(23 - c) + 11c = 263
299 - 13c + 11c = 263
-2c = -36
c = 18

there were 18 childrens



let x be the first number any y be the second
x + y = 70
y = 2x + 1


x + 2x + 1 = 70
3x = 69
x = 23

the two numbers are 23 and 47



let x be the number and y be the other
x = y + 12
y + 2x = 39

y + 2(y + 12) = 39
y + 2y + 24 = 39
3y = 15
y = 5

the larger number is 5 + 12 = 17


plug -2 for x
f(-2) = 5(-2)^2 - 3(-2) + 1
= 20 + 6 + 1
= 27



plug -4 for x
f(-4) = -4(-4) + 5
= 16 + 5
= 21

Answer 2

C = # of children
23-C = # of adults
11C +13(23-C) = 263
11C +299 -13 C = 263
-2C = -36
C= 18

x = one number
70 - x = other number
70-x = 2x+1
3x = 69
x = 23
70 - x = 47

x = 1st number
x+12 = 2nd number
x +2(x+12) = 39
3x + 24 = 39
3x = 15
x = 5
x+12 = 17 = larger nunber

f(-2) 5(-2)^2 - 3(-2) +1 = 20 +6 +1 = 27

f(-4) = -4(-4) +5 16+5 = 21