HW HELP NEEDED !

Question

If 101 people attend a concert and tickets for adults cost $2 while tickets for children cost $1.5 and total receipts for the concert was $167, how many of each went to the concert?

 adults

 children

Answer 1

Lets X be the number of adults, so the number of children will be 101 - X. We will find the total price for their ticket and put it equal to 167, to solve for X.

2 X + (101 -X) . 1.5 = 167

2 X - 1.5 X = 167 - 151.5

.5 X = 15.5

X = 31 which is the number of adults and 101 - 31 = 70 is the number of children.

Answer 2

If all attendees were adults the total receipts would have been $2 x 101 = $202

But as the receipts are only $167,

$202 - $167 = $35 are missing

$35 are missing because tickets for children cost $ 0.50 less than tickets for adults. It means that $35 / $0.50 = 70 tickets for children were sold.

If out of 101 attendees 70 were children, then there were 101 - 70 = 31 adults