Question

3/8 of people watching a play are adults. The rest of the people are watching are children. There are 32 more children than adults watching the play. How many people are watching the play in total?

Answer 1

This is a word problem on linear equations

Step by step explanation

Let the total number of people watching the play be represented by “y”

y= adults + children

Adults = 3/8 * y = 3y/8
Adults = 3y➗ 8
The rest are children
Children = Total - Adult
Children = y -( 3y/8)
Children = y - (3y ➗8)

Remember Children + Adult = Total

32+ Adult = number of children
32 + (3y/8) = y - (3y/8)
Solve for y
32 + (3y➗8) = y - (3y ➗ 8)
Multiply through by the lcm factor which is 8 or cross multiply
(32 x 8) + 8(3y➗8) = (8 x y) - 8(3y➗8)
256 + 3y = 8y - 3y
256 + 3y = 5y
256 = 5y - 3y
256 = 2y
256➗2= y
128= y


So the total number of people watching the play is 128 people

You can go further to cross check by finding the number of adults and children and comparing it to the question