Question

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

Answer 1

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.