Transcript Slide 1 - msmatthewsschs

(3.2b) NOTES- System Word Problems
Ex: The Steele Canyon drama club is putting on a
show. Student tickets cost $6 while adult tickets cost $8.
If 200 total tickets were sold for $1,440, how many of
those tickets were student tickets?
Let x= # of student tickets
Let y= # of adult tickets
Set up system:
 x  y  200

6x  8y  1440
 x  y  200

6x  8y  1440
Let x= # of student tickets
Let y= # of adult tickets
• the top equation represents amount of tickets.
• the bottom equation represents value.
• Solve the system using the substitution or
linear combination method.
• Re-read the problem to see what it is
specifically asking for.
-8 x + y = 200
6x + 8y = 1440
-8x – 8y = –1600
6x + 8y = 1440
–2x = -160
x = 80
80 + y = 200
y = 120
There were 80 student tickets sold.
1. The difference between two numbers is 11. The
larger number is 3 less than two times the smaller
number. Find the two numbers.
x – y = 11
x = 2y – 3
2y – 3 – y = 11
y – 3 = 11
y = 14
x = bigger #
y = smaller #
x = 2y – 3
x = 2(14) – 3
x = 28 – 3
x = 25
The two numbers are 25 and 14.
2. Your cousin gave you a collection of 70 movies. Some
are DVDs and the rest are VHS tapes. There are 6 more
VHS tapes than 3 times the number of DVDs. How
many of each type are in the collection.
D + V = 70
V = 3D + 6
D + 3D + 6 = 70
4D + 6 = 70
4D = 64
D = 16
D = # DVD’s
V = # VHS’s
V = 3D + 6
V = 3(16) + 6
V = 48 + 6
V = 54
There are 16 DVD’s and 54 VHS’s.
3. You invited 56 people to your graduation party. You
can afford to rent 5 tables, round and/or rectangular.
Each round table can seat 8 people and each rectangular
table can seat 12 people. How many round and
rectangular tables should you rent?
x = # round tables
y = # rect. tables
-8 x + y = 5
8x + 12y = 56
x+y=5
x+4=5
x=1
–8x – 8y = –40
8x + 12y = 56
4y = 16
y=4
There is 1 round table and 4 rectangular tables.
4. A soccer team bought ice-cream cones to celebrate a
victory. The total cost of 12 double cones and 8 single
cones was $17. A double cone cost $0.25 more than a
single cone. What was the price of each type of cone?
12D + 8S = 17
D = S + 0.25
12(S + 0.25) + 8S = 17
12S + 3 + 8S = 17
20S + 3 = 17
20S = 14
S = 0.70
D = Cost of double cone
S = Cost of single cone
D = S + 0.25
D = 0.70 + 0.25
D = 0.95
A single costs 70¢ and a double costs 95¢.