Answer:
a. x = licensed riders; y = junior racers
b. x + y = 321; 25x +15y = 6935
c. see attached. (x, y) = (212, 109); 212 licensed riders; 109 junior racers
Explanation:
You want to determine the number of racers of each type, given 321 racers total paid $6935 in fees. Licensed racers paid $25 each, and junior racers paid $15 each. You want a system of equations and a graphical solution.
a. Variables
In general, the variables represent the values the question is asking for. In part (b), we see that we want to find the number of racers of each type. Since our graphing program prefers the variables x and y, we will assign those in the same order the descriptions of the types of racers appear in the problem statement. (Keeping the order can avoid confusion later.)
x = the number of licensed riders
y = the number of junior racers
b. Equations
The relations given in the problem statement give rise to two equations:
- x + y = 321 . . . . . . . . . the total number of racers
- 25x +15y = 6935 . . . . the total income from fees
c. Graph
The attached graph shows the solution to these equations is (x, y) = (212, 109). There were 212 licensed riders and 109 junior racers.
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