There were 411 people at a play. Admission was $5 for adults and $3.75 for children. The receipts were $1978.75. How many adults and how many children attended Thanks so much!

A + C = 411
5A + 3.75C = 1978.75

times the first equation by 5 to get 5A + 5C = 2055

then do 5A + 5C = 2055 MINUS 5A + 3.75C = 1978.75

so you remain with:
1.25C = 76.25
C = 76.25/1.25 = 61

61 CHILDREN ATTENDED

now to figure out how many adults:
A + 61 = 411
A = 411-61 = 350

350 ADULTS ATTENDED