Solving systems of equations word problems worksheet For all problems, define variables, write the system of equations and solve for all variables.
-At the end of the 2000 baseball season, the New York Yankees and the Cincinnati Reds had won a total of 31 World Series. The Yankees had won 5.2 times as many World Series as the Reds. How many World Series did each team win?
Step by step please
Let's define:
x = number of World Series won by the Cincinnati Reds
y = number of World Series won by the New York Yankees
We can create a system of equations based on the given information:
1) x + y = 31 (The total number of World Series won by both teams is 31)
2) y = 5.2x (The Yankees won 5.2 times as many World Series as the Reds)
To solve this system of equations, we can use the substitution method. Let's solve equation (2) for y:
y = 5.2x
Now substitute this expression for y in equation (1):
x + 5.2x = 31
Combine like terms:
6.2x = 31
Divide both sides by 6.2:
x = 31/6.2
x = 5
So the Cincinnati Reds won 5 World Series.
Now substitute this value of x into equation (2) to find y:
y = 5.2x
y = 5.2 * 5
y = 26
Therefore, the New York Yankees won 26 World Series.
Step 1: Define the variables:
Let's define:
x = number of World Series won by the Cincinnati Reds
y = number of World Series won by the New York Yankees
Step 2: Write the system of equations:
We are given that the total number of World Series won is 31. This can be expressed as:
x + y = 31 ...(Equation 1)
We are also given that the Yankees won 5.2 times as many World Series as the Reds. This can be expressed as:
y = 5.2x ...(Equation 2)
Step 3: Solve the system of equations:
To solve the system of equations, we will use the substitution method.
Substitute Equation 2 into Equation 1:
x + 5.2x = 31
Combine like terms:
6.2x = 31
Divide both sides by 6.2 to isolate x:
x = 31/6.2
Simplify the right side:
x = 5
Now, substitute the value of x back into Equation 2 to find y:
y = 5.2(5)
y = 26
Step 4: Interpret the solution:
Our solution shows that the Cincinnati Reds won 5 World Series, while the New York Yankees won 26 World Series.
Step 1: Define variables
Let's define:
x = number of World Series won by the Cincinnati Reds
y = number of World Series won by the New York Yankees
Step 2: Write the system of equations
We have two pieces of information given in the problem. The first is that the total number of World Series won by both teams is 31. This gives us the equation:
x + y = 31
The second piece of information is that the Yankees won 5.2 times as many World Series as the Reds. Mathematically, this can be expressed as:
y = 5.2x
Step 3: Solve the system of equations
We can solve the system of equations using substitution or elimination method. Let's solve it using substitution.
Substitute the expression for y from the second equation into the first equation:
x + 5.2x = 31
Combine like terms:
6.2x = 31
Divide both sides by 6.2:
x = 5
Now substitute the value of x back into the second equation to find y:
y = 5.2(5)
y = 26
Step 4: Interpret the solution
According to the solution, the Cincinnati Reds won 5 World Series and the New York Yankees won 26 World Series.