Question

If 106 people attend a concert and tickets for adults cost four dollars what ticket for a children cost $3.75 and total receipt for the concert was $414 how much of each went to the concert

Answer 1

A = 66 adults, C = 40 children

Explanation:

We can set up a system of equations to find how many adults and how many children attended the concert, with A representing the adults and C representing the children:

`A + C = 106\\4A+3.75C=414`

We can use the elimination method and multiply everything in the first equation by -4

`-4(A+C=106)\\-4A-4C=-424\\4A+3.75C=414`

Once we add the values together, we're left with:

`-0.25C = -10`, where solving for C gives us C = 40

We can plug C into the first equation to find A:
`A+40=106`, where solving for A gives us A = 66