Solve the problem.
-Janet is planning to visit Arizona, New Mexico, and California on a 20-day vacation. If she plans to spend as much time in New Mexico as she does in the other two states combined, how can she allot her time in the three states? (Let $ x $ denote the number of days in Arizona, $ y $ the number of days in New Mexico, and $ z $ the number of days in California. Let $ z $ be the parameter.)
A) $ x=10, y=10-z, 0 \leq z \leq 10 $
B) $ x=10, y=z-10,0 \leq z \leq 10 $
C) $ x=z-10, y=10,0 \leq z \leq 10 $
D) $ x=10-z, y=10,0 \leq z \leq 10 $

Question

Quizplus · Accepted Answer

Janet spends as much time in New Mexico as in Arizona and California combined, so $ y = x + z $. The total time is 20 days, so $ x + y + z = 20 $. Substituting $ y = x + z $ gives $ x + (x + z) + z = 20 $, simplifying to $ 2x + 2z = 20 $, or $ x + z = 10 $. Thus, $ x = 10 - z $ and $ y = 10 $.

Solve the Problem x x x Denote the Number of Days in Arizona

Solve the Problem $x$ Denote the Number of Days in Arizona