A local dinner theater sells adult tickets for $105 and each children tickets for $ 60 each. for a certain show the theater sells 84 tickets for a total of $7,155. how many of each type of ticket were sold.
Let A be the number of adult tickets and C be the amount of children tickets. We can form the equation 105A + 60C = 7155, as we converted it from dollars to regular integers. We can simplify the equation by dividing by 5, giving 21A + 12C = 1431. Dividing by 3 gives 7A + 4C = 477. 477 divided by 7 gives 68 remainders 1, and if we remove one more seven and add it to one, we will have a multiple of 4. This means 67 adult tickets and 2 children tickets.