Hi
Could someone work this through out, with me?
J,M and C shared some sweets. the ratio of the total number of sweets recieved by J & M to the number recieved by C is 2:5
When C gave 25 sweets to J and 31 sweets to M and J gave 12 sweets to M, each of them has the same number of sweets.
Find out the total number of sweets J had first.
Thanks for your help
Start with what you are first given and assign variables. Since we want the number of sweet had at first (by J), define your variables for that time:
1) j is the number of sweets J had initially
2) m is the number of sweets M had initially
3) c is the number of sweets C had initially
Define you constants
a) r is the ratio = 2/5 = 0.4
Work the problem:
a) The ratio of the total number of sweets recieved by J & M to the number received by C is r gives the equation
(j + m) / c = r
or
j + m = r c
[Note: Some might interpret that statement as j/c = m/c = r but I don't think that is the correct interpretation. However I have been wrong several times in my life as the people around here can attest.]
b) When C gave 25 sweets to J and 31 sweets to M and J gave 12 sweets to M, each of them has the same number of sweets.
- C ended up with c - 25 - 31 (25 to J and 31 to M)
- J ended up with j + 25 - 12 (25 from C and 12 to M)
- M end up with m + 31 + 12 (31 from C and 12 from J)
and
c - 25 - 31 = j + 25 - 12 = m + 31 + 12
At the end how many does C have in terms of how much J has (what is c in terms of j). At the end how many does M have in terms of how much J has (what is m in terms of j). Use that information in the first equation [j+m=rc] to find out what j is.
