Question

1)An exam worth 172 points contains 30 questions. Some questions are worth 2 points, and the others are worth 9 points. How many 2 point and 9 point questions are on the test?
2) Tickets to the fair cost $6 for children and $13 for adults. On Saturday 163 people
enter the fair and they collected $1566. What number of children and what number
of adults attended?

3) Tickets at a particular movie theater have different rates for adults and children.
On Saturday the theater sold 8 adult tickets and 7 child tickets for $132. The next
day, the theater sold 4 adult tickets and 5 children tickets for $72. What is the price
for the adult ticket and the price for the child ticket?

Answer 1

1) x+y=302x+9y=172x=-y+30-2y+60+9y=1727y=112y=16x=14
14 2-point questions and 16 9-point questions
2) c+a=163
6c+13a=1566
c=-a+163
-6a+976+13a=1566
7a=588
a=84
c=79
84 adult tickets and 79 children tickets
3) a+c=15; ax+cy=132
8+7=15; 8x+7y=132

a+c=9; ax+cy=72
4+5=9; 4x+5y=72

8x+7y=132
4x+5y=72
(8x+10y)=(144)

8x=-7y+132
8x=-10y+144
-7y+132=-10y+144
3y=12
y=4
4x+20=72
4x=52
x=13
The price for an adult ticket is $13 and the price for a child ticket is $4