Question

She charged $6.25 per infant, and $9.50 for any child over the age of 3. She earned a total of $245.50 while babysitting for 32 children. How many infants and how many children over 3 did she babysit?

A) 12 infants and 20 children over 3
B) 15 infants and 17 children over 3
C) 18 infants and 14 children over 3
D) 20 infants and 12 children over 3

Answer 1

The problem is solved using a system of equations to determine the number of infants and children over 3 babysat, based on the total earned and rates charged. The babysitter watched 18 infants and 14 children over 3, which matches option C.

Step-by-step explanation:

The problem stated involves determining the number of infants and children over 3 that were babysat given the total amount earned and the rates charged per infant and child over 3. Let's define two variables: let i be the number of infants and c be the number of children over 3. We have two pieces of information:

• The total number of children is 32: i + c = 32.
• The total amount earned is $245.50: 6.25i + 9.50c = 245.50.

We can solve these equations to find the values of i and c. Here are the steps:

1. Rewrite the first equation as i = 32 - c and substitute in the second equation.
2. This gives us 6.25(32 - c) + 9.50c = 245.50.
3. Simplify and solve for c: 200 - 6.25c + 9.50c = 245.50.
4. The resulting equation is 3.25c = 45.50.
5. Divide by 3.25 to find c equals approximately 14.
6. Then use i = 32 - c to find i equals approximately 18.

Therefore, the babysitter watched 18 infants and 14 children over 3 years old. This corresponds to option C.