Question

The fees collected for a workshop was $327. Each adult paid $15 and each child paid $9 to attend the workshop. There were 7 more children than adults. How many people attended the workshop in all?​

Answer 1

29

Explanation:

We know that the total amount collected was $327.

We also know that each adult (represented by a) paid $15, and each child (represented by c) paid $9. There were 7 more children (c) than adults (a).

We can write an equation:

15a+9(a+7)=327

simplify

15a+9a+63=327

simplify

24a+63=327

subtract 63 from both sides

24a=264

divide both sides by 24

a=11

So, 11 adults attended the workshop. We can figure out how many children attended because there were 7 more children than adults:

11+7

=18

So, 18 children attended the workshop. The total number of people that attended was:

11+18

=29

Hope this helps! :)

Answer 2

29 attended in all

Explanation:

let a represent the number of adults and c the number of children, then

15a + 9c = 327 → (1)

given there were 7 more children than adults, then

c = a + 7 → (2)

substitute c = a + 7 into (1)

15a + 9(a + 7) = 327 ← distribute parenthesis and simplify left side

15a + 9a + 63 = 327

24a + 63 = 327 ( subtract 63 from both sides )

24a = 264 ( divide both sides by 24 )

a = 11

substitute a = 11 into (2)

c = 11 + 7 = 18

no of people attending = a + c = 11+ 18 = 29