4. 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?
Let's define:
- x as the number of World Series won by the Reds
- y as the number of World Series won by the Yankees
We know that the total number of World Series won by both teams is 31, so we can create the following equation:
x + y = 31
We also know that the Yankees won 5.2 times as many World Series as the Reds, which can be represented by the equation:
y = 5.2x
Now we can solve this system of equations using substitution or elimination.
Substitution Method:
Substitute the value of y from the second equation into the first equation:
x + 5.2x = 31
6.2x = 31
x = 31/6.2
x ≈ 5
Substitute the value of x back into the second equation to find y:
y = 5.2(5)
y = 26
Therefore, the Reds won approximately 5 World Series and the Yankees won approximately 26 World Series.
Step 1: Define variables:
Let's define x as the number of World Series won by the Cincinnati Reds.
Let's define y as the number of World Series won by the New York Yankees.
Step 2: Write the system of equations:
From the problem, we know that:
1) The total number of World Series won by both teams is 31: x + y = 31
2) The Yankees won 5.2 times as many World Series as the Reds: y = 5.2x
Step 3: Solve the system of equations:
We can solve this system of equations using substitution or elimination method.
Substitution Method:
Substitute the value of y from equation 2) into equation 1):
x + 5.2x = 31
6.2x = 31
Divide both sides by 6.2:
x = 31/6.2
x = 5
Now substitute the value of x into equation 2) to find y:
y = 5.2(5)
y = 26
Step 4: Answer:
The Cincinnati Reds won 5 World Series and the New York Yankees won 26 World Series.
To solve this word problem involving systems of equations, we need to define variables and set up a system of equations.
Let's define:
x = the number of World Series won by the Reds
y = the number of World Series won by the Yankees
We know that the total number of World Series won by both teams is 31. Therefore, our first equation is:
x + y = 31 -- Equation 1
It is also given that the Yankees won 5.2 times as many World Series as the Reds. Mathematically, this can be expressed as:
y = 5.2x -- Equation 2
Now, we have a system of equations: Equation 1 and Equation 2.
To solve the system of equations, we can use the substitution or elimination method. Let's use the substitution method in this case.
Substituting Equation 2 into Equation 1, we get:
x + 5.2x = 31
Combining like terms, we have:
6.2x = 31
Dividing both sides of the equation by 6.2, we can solve for x:
x = 31/6.2
x = 5
Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y.
Using Equation 2:
y = 5.2x
y = 5.2(5)
y = 26
Therefore, the Reds won 5 World Series, and the Yankees won 26 World Series.