Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

Anita and Todd are hosting events that are catered by the same company. Anita plans to have 78 adults and 70 children attend, so the total projected cost of her meals is $2,946. Todd has 76 adults and 31 children on her guest list, so he will pay the caterer $2,424. How much does the caterer charge for each meal?

Every adult's meal costs $, and every child's meal costs $.