Question

the area of a bus park is 1500
square meters. The
park is strictly for buses and personal cars. An area of 45 square meters is
allowed for a bus and 25 square meters
for a personal car. The number of buses as estimated is always not less than one
third and not more than two thirds the number of personal cars. If x is the number of buses and y the number of personal
cars, which is following inequality represents either of the scenarios.​

Answer 1

Given :   area of a bus park is 1500 square meters. The park is strictly for buses and personal cars. An area of 45 square meters is allowed for a bus and 25 square meters for a personal car. The number of buses as estimated is always not less than one third and not more than two thirds the number of personal cars.   x is the number of buses and y the number of personal cars,

To Find : inequalities

Solution:

Buses = x

Cars  = y

45x + 25y  ≤ 1500

=> 9x + 5y ≤ 300

The number of buses as estimated is always not less than one

third and not more than two thirds the number of personal cars

=>   y/3 ≤ x  ≤ 2y/3

=>  y ≤ 3x  ≤  2y

=> 3y  ≤ 9x  ≤  6y

Adding 5y both sides

=>  3y + 5y  ≤ 9x  + 5y  ≤  6y  + 5y

=> 8y   ≤ 9x  + 5y  ≤  11y

              9x + 5y  ≤ 300

=> 8y  ≤ 300

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Answer 2

Step-by-step explanation:

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