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?
Step by step please
Let's define the variables:
Let A be the amount Troy Aikman earned.
Let D be the amount Deion Sanders earned.
We can create two 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)
Now, we can solve the system of equations.
Let's substitute equation 1 into equation 2:
(D + 0.467) + D = 12.867
Combine like terms:
2D + 0.467 = 12.867
Subtract 0.467 from both sides:
2D = 12.867 - 0.467
2D = 12.4
Divide both sides by 2:
D = 12.4 / 2
D = 6.2
Now, substitute the value of D into equation 1 to find A:
A = 6.2 + 0.467
A = 6.667
Therefore, Deion Sanders earned $6.2 million and Troy Aikman earned $6.667 million during the 1999 season.
To solve this word problem, first, define variables to represent the unknowns in the problem. Let's define:
Let's assume the amount Deion Sanders earned to be x million dollars.
Troy Aikman, the quarterback, earned $0.467 million more than Deion Sanders, so his earnings can be represented as (x + 0.467).
The problem states that together they cost the Cowboys $12.867 million, so the equation can be set up as follows:
x + (x + 0.467) = 12.867
Now, let's solve this equation step by step:
1. Combine like terms: x + (x + 0.467) = 12.867 becomes 2x + 0.467 = 12.867.
2. Subtract 0.467 from both sides of the equation to isolate 2x: 2x + 0.467 - 0.467 = 12.867 - 0.467. This simplifies to 2x = 12.4.
3. Divide both sides by 2 to solve for x: 2x/2 = 12.4/2. This gives us x = 6.2.
So, Deion Sanders earned $6.2 million.
To find Troy Aikman's earnings, plug the value of x back into the expression (x + 0.467):
Troy Aikman's earnings = 6.2 + 0.467 = 6.667 million.
Therefore, Deion Sanders earned $6.2 million, and Troy Aikman earned $6.667 million.
Step 1: Define Variables:
Let's define:
- Troy Aikman's salary as A (in millions)
- Deion Sanders' salary as D (in millions)
Step 2: Write the System of Equations:
From the problem, we know:
1. Troy Aikman earned $0.467 million more than Deion Sanders.
A = D + 0.467 (Equation 1)
2. Together they cost the Cowboys $12.867 million.
A + D = 12.867 (Equation 2)
Step 3: Solve for All Variables:
To solve this system of equations, we can use the 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
Divide both sides of the equation by 2:
D = 12.4 / 2
D = 6.2
Now substitute the value of D back into Equation 1:
A = 6.2 + 0.467
A = 6.667
Therefore, Deion Sanders earned $6.2 million and Troy Aikman earned $6.667 million.