Evaluate different parts of the expression separately.
95.0
Practice makes perfect
The formula that calculates the efficiency rating of a quarterback has several parts and involves several variables.
Let's first summarize the information given on Peyton Manning's card.
Variable
Description
Value
C
Passes Completed
371
A
Passes Attempted
555
Y
Passing Yardage
4002
T
Touchdown Passes
27
I
Interceptions
12
The efficiency rating formula involves a sum of four terms multiplied by 1006.
(
C/A-0.3/0.2+
Y/A-3/4+
T/A/0.05+
0.095-I/A/0.04
)
* 100/6Let's use the order of operations. We will calculate the four terms separately inside the parentheses, add them up, and then finish with the multiplication outside of the parentheses.
Let's start with the first term.
We can find the other terms in a similar way. The table below contains the results.
Term
Expression
Value
C/A-0.3/0.2
371/555-0.3/0.2
409/222
Y/A-3/4
4002/555-3/4
779/740
T/A/0.05
27/555/0.05
36/37
0.095-I/A/0.04
0.095-12/555/0.04
543/296
The next step is to add these numbers. Remember to find their common denominator before adding them.
409/222+779/740+36/37+543/296=25 319/4440
As a final step, the formula calls for multiplying the result by 1006.
25 319/4440* 100/6=12 6595/1332
This is the exact value of Peyton Manning's efficiency rating for the 2008 season. The question asks for this rating as a decimal rounded to the nearest tenth, so we need to find the quotient and round the decimal number.
Efficiency Rating:12 6595/1332≈ 95.0
