Maths-
General
Easy

Question

Jackie has two summer jobs. She works as a tutor, which pays $12 per hour, and she works as a lifeguard, which pays $9.50 per hour. She can work no more than 20 hours per week, but she wants to earn at least $220 per week. Which of the following systems of inequalities represents this situation in terms of x and y, where x is the number of hours she tutors and y is the number of hours she works as a lifeguard?

  1. table attributes columnalign right columnspacing 0em end attributes row cell 12 x plus 9.5 y less or equal than 220 end cell row cell x plus y greater or equal than 20 end cell end table
  2. table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 12 x plus 9.5 y less or equal than 220 end cell row cell x plus y less or equal than 20 end cell end table
  3. table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 12 x plus 9.5 y greater or equal than 220 end cell row cell x plus y less or equal than 20 end cell end table
  4. table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 12 x plus 9.5 y greater or equal than 220 end cell row cell x plus y greater or equal than 20 end cell end table

Hint:

Hint:- Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The correct answer is: table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 12 x plus 9.5 y greater or equal than 220 end cell row cell x plus y less or equal than 20 end cell end table


    Solution:-
    • We have given that Jackie has two jobs. She works as a tutor and lifeguard.
    • Payment as a tutor =  $12 per hour
    Payment as a lifeguard = $9.50 per hour
    • x = Number of hours she tutors.
    y = Number of hours she works as lifeguard.
    • Then amount as tutor will be calculate by multiplying number of hours, x and payment per hour, which will be 12x and same for lifeguard i. e 9.5y   
    Therefore, total amount earned per week will be 12x + 9.5y
    • Minimum payment she requires= $220 per week.
    Therefore,       12x + 9.5y ≥ 220
    • Maximum work in a week= 20 hours
    Therefore,        x + y ≤ 20
    Therefore, the correct option is C) 12x + 9.5y ≥ 220
    x +y  ≤ 20

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