What's wrong with my calculation?

[38175425]

"Tom ate one-third of the candies in a box. Roger ate two-fifths of the reamaining candies. There were 18 candies left. How may candies were in the box to start with?"
Here's how I calculate:
Let n = numbers John start with
2/3n - 3/5(2/3n) = 18
2/3n - 6/15n = 18
10/15n - 6/15n = 18
4/15n = 18
1/15n = 4.5
15/15n = 67.5
But I checked, the answer is 45 candies. But I don't know why.

 

[Deleted member 4993]

"Tom ate one-third of the candies in a box. Roger ate two-fifths of the reamaining candies. There were 18 candies left. How may candies were in the box to start with?"
Here's how I calculate:
Let n = numbers John start with
2/3n - 3/5(2/3n) = 18
2/3n - 6/15n = 18
10/15n - 6/15n = 18
4/15n = 18
1/15n = 4.5
15/15n = 67.5
But I checked, the answer is 45 candies. But I don't know why.

Let's check the given answer.

Starting #of candies = 45

Tom ate 1/3 of that \(\displaystyle \to \ \ \ \) Tom ate (1/3 * 45 =) 15 candies \(\displaystyle \to \ \ \ \) candies left (= 45 - 15 =) 30 \(\displaystyle \to \ \ \ \)

Roger ate two-fifths of the reamaining candies \(\displaystyle \to \ \ \ \) Roger ate [2/5 * 30 =] 12 candies \(\displaystyle \to \ \ \ \) candies left (= 30 - 12 =) 18

Now check your work again .... do you see the problem?

 

[HallsofIvy]

"Tom ate one-third of the candies in a box. Roger ate two-fifths of the reamaining candies. There were 18 candies left. How may candies were in the box to start with?"
Here's how I calculate:
Let n = numbers John start with

The problem, as you state it, mentions only "Tom" and "Roger". Who the heck is "John"? And it really makes no sense to say "n= numbers". You mean "Let n= number of candies in the box originally". On the other hand, kudos for actually stating what "n" is intended to represent.

2/3n - 3/5(2/3n) = 18

It would be better to say how you got this equation. (And would shock your teacher!)
Since Tom ate 1/3 of the candies, there were 2/3 left. Then Roger ate 2/5 of that: 2/5 of 2/3 is (2/3)(2/5)= 4/15. NOT 6/15. That is your error.

2/3n - 6/15n = 18

So this should be (2/3)n- (4/15)n= 18.
(Notice the parentheses. "2/3n" is, properly "2 divided by 3n", not "2/3 of n".)
Now (10/15)n- (4/15)n= (6/15)n= (2/5)n= 18 so n= (5/2)(18)= 5(9)= 45.

Check: If there were 45 candies in the box, 1/3 of 45 is 15 so Tom ate 15 candies, leaving 30. Roger ate 2/5 of 30= 12. 30- 12= 18.

10/15n - 6/15n = 18
4/15n = 18
1/15n = 4.5
15/15n = 67.5
But I checked, the answer is 45 candies. But I don't know why.

 

[38175425]

My problem is solved thank you

 

[lookagain]

So this should be (2/3)n- (4/15)n= 18.
(Notice the parentheses. "2/3n" is, properly "2 divided by 3n", not "2/3 of n".) **

** Actually, it is 2/3 of n. It is the constant 2/3 multiplied by the variable n.
By the Order of Operations, 2 is divided by 3. That result is multiplied by n.

Anytime I write a fraction, such as 2/3, as a coefficient in horizontal form,
however, I will be sure to use grouping symbols for better readability/clarity:

(2/3)n

For 2 to be divided by (3n) in horizontal style in one term, grouping symbols
are needed in the denominator:

2/(3n)