Chapter 9 - XYZ Custom Plus

560
Chapter 9 Solving Equations and Inequalities
2. Use the formula in Example 2 to
find C
when
F
is 77 degrees.
Note
The formula we are
using here,
C 5 }}
5 9 } (F 2 32),
is an alternative form of the formula
we mentioned in the introduction
to this section:
F 5 }}
9 5 } C 1 32
Both formulas describe the same
relationship between the two
temperature scales. If you go on
to take an algebra class, you will
learn how to convert one formula
into the other.
3. Use the formula in Example 3 to
find y when
x
is 0.
ExAmplE 2
Use the formula C 5 } 5 9
degrees.
}(F 2 32) to find C when F
is 95
SOlutiOn Substituting 95 for F
in the formula gives us the following:
When F 5 95
the formula C 5 5 } 9
(F 2 32)
becomes C 5 5 } 9
(95 2 32)
5 5 } 9
(63)
5 5 } 9
? 63 } 1
5 315 } 9
5 35
A temperature of 95 degrees Fahrenheit is the same as a temperature of 35 degrees
Celsius.
ExAmplE 3
Use the formula y 5 2x 1 6 to find y
when
x is 22.
SOlutiOn Proceeding as we have in the previous examples, we have:
When x 5 22
the formula y 5 2x 1 6
becomes y 5 2(22) 1 6
5 24 1 6
5 2
In some cases evaluating a formula also involves solving an equation, as the next
example illustrates.
4. Use the formula in Example 4 to
find y
when
x is 23.
ExAmplE 4
SOlutiOn
for y.
Find y when
x
is 3 in the formula 2x 1 3y
5 4.
First we substitute 3 for x ; then we solve the resulting equation
When x 5 3
the equation
becomes
2x 1 3y
5 4
2(3) 1 3y
5 4
6 1 3y
5 4
3y
5 22 Add −6 to each side
y 5 2 2 } 3
Divide each side by 3
Answers
2. 25 degrees Celsius 3. 6
4. }}
1 }
0
3
b Rate Equation
Now we will look at some problems that use what is called the rate equation. You
use this equation on an intuitive level when you are estimating how long it will
take you to drive long distances. For example, if you drive at 50 miles per hour for
2 hours, you will travel 100 miles. Here is the rate equation:
Distance 5 rate ? time, or d 5 r ? t