2070.23 – Babysitting Rates

Holly gets $2.00 per hour for the first child in the family, while they are awake. She gets $1.50/hour while the child is asleep. Additional children, awake or asleep, increase her wage by $1.00 per hour for each child. Develop a formula to calculate her wage based on nn children for xx hours before bedtime and yy hours after bedtime.

Solution

For the first child, Holly gets 2x+1.5y2x+1.5y per hour. Assuming that n≥1n\geq 1, any extra children net her (n−1)(x+y)(n-1)(x+y). The total is 2x+1.5y+(n−1)(x+y)=(n+1)x+(n+.5)y2x+1.5y+(n-1)(x+y) = (n+1)x + (n+.5)y.