Answer to Question #138881 in Algebra for Prestyn

Question

You work as a cashier for a grocery store and earn $6 per hour. You also mow lawns and earn $3 per hour. You want to earn at least $30 per week but you would like to work no more than 12 hours per week. Which system is the solution of the real-world problem

Answer 1

Let the number of hours taken at the store be x,

the number taken at the lawns be y

hence:

working no more than 12 hours is

x + y ≤  12

hence: y ≤ 12 - x            equation 1

earning at least $30 per week is:

$6 multiplied by the numbers of hours in the store

hence :$6 * x= $6x

$3 multiplied by the number of hours at the lawns

hence :$3 * y =$3y

 therefore : $6x +$3y ≥ $30         equation 2

which is also $2x +$ y ≥ $10

$y ≥ $10 -$2x

hence the system that provide possible solutions is:

$12 -x ≥ y ≥ $10 -$2x