Answer:
Johnson's class earned More money then Smith's class
and amount of more money earned is $44.5
Step-by-step explanation:
Given:
Mrs Johnson Class sold cookies for $2.50 each
Mr Smith class sold pop corn for $1.50 each
Total Items Sold = 53
Total money earned = 105.50
To Find:
Which class earned more money and how much = ?
Solution:
Let x denotes the cookies sold and y denotes the popcorn sold
Now
Money earned by Johnson's class = $2.50 * x
Money earned by Smith's class = $1.50 * y
Total items sold = 51
And it could be written as
Total Cookies sold + total pop corns sold = 51
i.e
x + y = 51 ...............(i)
Now
Total earned = $ 105.50
which is
Total earned by cookies + total earned by popcorn = $ 105.50
i.e.
2.50 * x + 1.50 * y = 105.50 ............(ii)
From equation (i) we have
x + y = 51
or
x = 51 - y .............(iii)
Putting this value in equation (ii) which is
2.50 * (51-y) + 1.50 * y = 105.50
127.50 - 2.50 y + 1.50 y = 105.50
It becomes
127.50 - y = 105.50
Now subtracting 127.50 from both sides
127.50 - 127.50 -y = 105.50 - 127.50
- y = -22
or
y=22
Pop corns sold = 22
Now from equation (iii) we have
x = 53 - 22
x = 31
Cookies Sold = 31
Now
Money earned by Johnson's class = $2.50 * x
= 2.50 * 31
= $ 77.5
Money earned by Smith's class = $1.50 * y
= 1.50 * 22
=$ 33
So Johnson's class earned more money
More money earned = 77.5 - 33
=$44.5
