Shannon ate 1/4 of a box of chocolates and Shane ate 1/2 of what was left. If only 15 chocolates remained, how many chocolates were originally in the box?
+23254 Let n represent the number of chocolates in the box.
Since Shannon ate 1/4 of the chocolates, she ate (1/4)x.
The number remaining is (3/4)x.
Shane ate 1/2 of what was left, so Shane ate (1/2) of (3/4)x, or (3/8)x.
Total number of chocolates = Shannon's + Shane's + 15.
Since the total number is n: n = (1/4)n + (3/8)n + 15
Multiply all the terms by 8: 8n = 2n + 3n + 120
---> 8n = 5n + 120
---> 3n = 120
---> n = 40.
Shannon's share = (1/4)(40) = 10.
Shane's share = (3/8)(40) = 15.
My share = those that are left = 15.
Total = 40.
+23254 Let n represent the number of chocolates in the box.
Since Shannon ate 1/4 of the chocolates, she ate (1/4)x.
The number remaining is (3/4)x.
Shane ate 1/2 of what was left, so Shane ate (1/2) of (3/4)x, or (3/8)x.
Total number of chocolates = Shannon's + Shane's + 15.
Since the total number is n: n = (1/4)n + (3/8)n + 15
Multiply all the terms by 8: 8n = 2n + 3n + 120
---> 8n = 5n + 120
---> 3n = 120
---> n = 40.
Shannon's share = (1/4)(40) = 10.
Shane's share = (3/8)(40) = 15.
My share = those that are left = 15.
Total = 40.
