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Sandra is paid an hourly base rate for babysitting up to two children a day, and an additional 20% per hour for each additional child. If her hours are rounded up to the next full hour, how many hours was Sandra paid for last week?

1) One day last week, Sandra was paid $51 to babysit 3 children for 5 hours.
2) Sandra was paid a total of $108.80 last week and never babysat more than 3 children at once.

OA C

Say the hourly rate is $x for babysitting up to two children a day; thus, the hourly rate would be $x + 20% of x = $1.2x for babysitting for three children a day and so on.

Let's take each statement one by one.

1) One day last week, Sandra was paid $51 to babysit 3 children for 5 hours.

=> 1.2x*5 = 51 => x = $8.50.

Can't get the information for the week. Insufficient.

2) Sandra was paid a total of $108.80 last week and never babysat more than 3 children at once.

Say Sandra babysat for one or two children in a week for m hours and did for three children in the week for n hours. We have to get the value of m + n.

Thus, xm + 1.2xn = 108.80

Can't get the information for the week. Insufficient.

(1) and (2) together

From (1), we know that x = $8.50 and n ≥ 5

Thus, from (2), we have 8.5m + 1.2*8.5n = 108.80 => 8.5m + 10.2n = 108.80

=> 85m + 102n = 1088

Note that m and n are positive integers given that her hours are rounded up to the next full hour.

So the task is to find out a unique combination of m and n such that n ≥ 5. Let's focus on 85m. Since the units digit of 85 is 5, the units digit of 85m would be either 0 or 5. Thus, the units digit of (1088 – 85m) would be 8 or 3. This means that the units digit of 102n must be 8 or 3. Trying out a few random values for n such that 5 ≤ n ≤ 10. You would note that 102n ≤ 1088, thus, n ≤ 10.

The only qualifying value of n (5 ≤ n ≤ 10) would work, and i.e. n = 9. Note that 102n = 102*9 => units digit 8. Thus, n = 9 hrs. Thus, 85m + 102n = 1088 => 85m + 102*9 = 1088 => 85m = 1088 – 918 = 170 => m = 170/85 = 2 hrs. Thus, m + n = 2 + 9 = 11 hrs. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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