### 3-5d - APAblog.org

```Write and Solve a System of Equations
Refer to the application at the beginning of the lesson. Write and solve
of equations to determine how many seats are in each section of the
amphitheater.
CONCERTS
a system
:
seats in section A
= seats in section B
z = lawn seats
ir
Understand Define the variables.
/
eReal-World Career
Plan There are 19,200 seats.
x+V+z:79,200
Music Management
Music management
involves acting as the
talent manager to the
arlists. Other duties
include negotiating with
record labels, music
promoters, and tour
promoters. Managers
The total revenue is \$456,000.
Equation t
30x+25y*202:456,000
Equation 2
There are twice as many seats in section B as in section A.
A
Solve
usually earn a percentage
:2x
Solve the system.
Step
of the artist's income.
Equation 3
t
Substitute a
:2x
in the first two equations.
x+y+z=79,200
A bachelor's degree
Equation I
xl2x*z:79,200
is usually required.
Y:Dt
3x+z=L9,200
+ 25y t 20z = 456,000 Equation 2
30x
30x
+ 25(2x)
80x
Step
2
Solve the system of two equations in two variables.
3x + z
look for a Pattern
+ZOz:456,000 y:2sr
+ 202:456,000 Simplify.
80x
+
= t9,200
IIiilElFFil
'
202:456,000
2oz = _a84,000
(+) 80x + 202:456,000
_-60x
20x
Looking for a pattern
can help to identify a
:72,000
r
:
3600
function and write an
equation.
Step
I
Substitute to find z.
3x + z :79,200
3(3600)
10,800
Step
4
*
*
z
z
:79,200
:79,200
z
:8400
,:
:
*I
--!--.-
1600
Distribute.
Simplifu.
Substitute to find y.
,,U-LA
_ 4..
:
Remaining equation in two variables
x:
ZpeOOl
Equation 3
or 7200
x
=
3600
The solution is (3600, 7200, 8400). There are 3600 seats in section A,
7200 in section B, and 8400 lawn seats.
Check Substitute the values into either of the first two equations.
Guided Practice
j 5. Ms. Garza invested \$50,000 in three different
,
,
,
accounts. She invested
three times as much money in an account that paid 8% interest than an
u..orrlt that paid 107o interest. The third account earned 12% interest. If
she earned a total of \$5160 in interest in a year, how much did she invest
in each account?
b
17O
Chapter 3 Systems of Equations and lnequalities
Personal Tutor slencoe.com
```