This question can be solved using an Algebraic equation.
The system of equations is given as:
x + y ≤ 10
8x + 16y ≥ 96
Let's represent
x = number of hours he walks the dogs
y = number of hours he works as a maths tutor
John must work for no more than 8 hours walking the dog and 2 hours as a Maths tutor to earn at least $96.
Our system of equations is given as:
He wants to work no more than 10 hours.
No more is represented by the inequality "≤ " = Less than or equal to
x + y ≤ 10 ...........Equation 1
He also wants to earn at least 96.
At least is represented by the inequality" ≥" = Greater than or equal to
$8 × x + $16 × y ≥ 96
8x + 16y ≥ 96........Equation 2
Solving for the number of hours
x + y = 10
x = 10 - y
Substitute 10 - y for x in Equation 2
8(10 - y) + 16y = 96
80 - 8y + 16y = 96
Collect like terms
8y = 96 - 80
8y = 16
Divide both sides by 8
8y/8 = 16/8
y = 2 hours
Solving for x
x = 10 - y
x = 10 - 2
x = 8 hours
Therefore, John must work for no more than 8 hours walking the dog and 2 hours as a Maths tutor to earn at least $96.
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