5. Solving systems of equations word problems worksheet For all problems, define variables, write the system of equations and solve for all variables.
-During the National Football League’s 1999 season, Troy Aikman, the quarterback for the Dallas Cowboys, earned $0.467 million more than Deion Sanders, the Cowboys cornerback. Together they cost the Cowboys $12.867 million. How much did each player make?
Let's define variables:
Let A be the amount Troy Aikman earned (in millions)
Let D be the amount Deion Sanders earned (in millions)
From the problem, we know the following information:
1. Troy Aikman earned $0.467 million more than Deion Sanders, so A = D + 0.467
2. The total cost of both players was $12.867 million, so A + D = 12.867
We have a system of equations:
A = D + 0.467
A + D = 12.867
To solve this system, we can use substitution or elimination method. Let's use substitution method by substituting the value of A from the first equation into the second equation:
(D + 0.467) + D = 12.867
2D + 0.467 = 12.867
2D = 12.867 - 0.467
2D = 12.40
D = 12.40/2
D = 6.20 million
Now, substitute the value of D into the first equation to find A:
A = 6.20 + 0.467
A = 6.667 million
So, Troy Aikman earned $6.667 million and Deion Sanders earned $6.20 million.
Step 1: Define variables
Let's define the following variables:
- Let "A" be the amount of money Troy Aikman earned (in million dollars).
- Let "D" be the amount of money Deion Sanders earned (in million dollars).
Step 2: Write the system of equations
Based on the given information, we can write the following two equations:
Equation 1: A = D + 0.467 (Troy Aikman earned $0.467 million more than Deion Sanders)
Equation 2: A + D = 12.867 (Together they cost the Cowboys $12.867 million)
Step 3: Solve for all variables
To solve the system of equations, we can use substitution or elimination method. Let's use substitution method:
Substitute Equation 1 into Equation 2:
(D + 0.467) + D = 12.867
2D + 0.467 = 12.867
2D = 12.867 - 0.467
2D = 12.4
D = 12.4 / 2
D = 6.2
Substitute the value of D into Equation 1:
A = 6.2 + 0.467
A = 6.667
Step 4: Interpret the results
Therefore, Deion Sanders earned $6.2 million, and Troy Aikman earned $6.667 million during the 1999 season.
To solve this problem, we need to define variables, write the system of equations, and then solve for all variables.
Let's define:
A = Troy Aikman's earnings (in millions)
D = Deion Sanders' earnings (in millions)
Now, we can write the system of equations based on the given information:
1) A = D + 0.467 (Troy Aikman earned $0.467 million more than Deion Sanders)
2) A + D = 12.867 (Together, they cost the Cowboys $12.867 million)
To solve this system of equations, we'll use the method of substitution or elimination.
Let's start with substitution:
From equation 1, we can substitute A = D + 0.467 into equation 2:
(D + 0.467) + D = 12.867
Simplifying the equation:
2D + 0.467 = 12.867
2D = 12.867 - 0.467
2D = 12.4
D = 12.4 / 2
D = 6.2
Now, we know Deion Sanders' earnings are $6.2 million.
Substitute this value back into equation 1 to find Troy Aikman's earnings:
A = 6.2 + 0.467
A = 6.667
Therefore, Troy Aikman made $6.667 million.
So, Deion Sanders made $6.2 million and Troy Aikman made $6.667 million.