Could you please assist with this Question I would like to confirm my answers and the working- thank you

Suppose that households have one child each and an income of M per year to spend on their child's education and other goods. Each year they elect to either send their children to a Public School and receive $21,000 worth of education or to a Private School and pay $X to receive $14,000+$X worth of education. For example, if a household chooses to spend X=$5,000 on private education, then they receive $19,000 in education.