
a.
To write the system of equations that represents the number of U.S. teams and non-U.S. teams.
a.

Answer to Problem 31PPS
Explanation of Solution
Given:
Number of professional mountain bike racing teams: 66
Number of non-U.S. teams is 30 more than the number of U.S. teams.
Calculation:
Let x represent the number of non-U.S. teams and y represent the number of U.S. teams.
The total number of professional mountain bike racing teams is 66.
So, it can be represented as:
Also, the number of non-U.S. teams is 30 more than the number of U.S. teams. Then,
Conclusion:
Therefore, the equations that represent the U.S. and Non-U.S. teams are
b.
To find the solution to the system of equations found in (a).
b.

Answer to Problem 31PPS
Explanation of Solution
Given:
From subpart (a),
The system of equations is:
Calculation:
Let the equations be labelled as follows:
Add the above equations.
Substitute
Say, Equation (2),
Conclusion:
Therefore, the solutions of the system of equations is
c.
To interpret the solution as the context of the question
c.

Answer to Problem 31PPS
Non-U.S. teams: 48
U.S. teams: 18
Explanation of Solution
Given:
From subpart (b),
Calculation:
Let x represent the number of non-U.S. teams and y represent the number of U.S. teams.
Then the number of non-U.S. teams is 48
The number of U.S. teams is 18.
Conclusion:
Therefore, the number of non-U.S. teams and U.S. teams are 48 and 18 respectively.
d.
Graph the system of equations and check the solution.
d.

Explanation of Solution
Given:
From subpart (a),
The system of equations is:
Graph:
Using a graphing utility the system of equations is graphed as follows:
Interpretation:
From the above graph, the point of intersection of x and y co-ordinates is the same as the solutions found algebraically.
Conclusion:
Therefore, the solutions of the equations are verified graphically.
Chapter 6 Solutions
Algebra 1
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