There were 114 tins in three cartons, P, Q and R altogether. If the shopkeeper moves 25 tins from P to Q, then 18 tins from Q and R, and finally 30 tins from R to P, there will be an equal number of tins in each carton. How many tins were there in each of the carton at first?
Please show working... Thx
2007-07-10 21:24:37 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
p + q + r = 114...........eq. A
p+5 = q + 7 = r - 12
p = q + 2
p = r - 17
substitute the above 2 equations in eq. A to get two new equations in terms of q and r..
2q + r = 112
q + 2r = 131
multiply the 1st eq. by 2 and subract the equations,
3q = 93
q = 31
r = 112 - 62
r = 50
Now substitute q and r in eq. A to get p,
p = 114 - 31 - 50
p = 33
P = 33, Q = 31 and R = 50
there u go.
2007-07-10 21:32:51 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Let P, Q and R be the number of tins in each carton to start with. We haveP + Q + R = 114
He moves 25 tins from P to Q, 18 from Q to R and 30 from R to P. So, P becomes P + 5, Q becomes Q + 7 and R becomes R -12. All of them are equal and are 1/3 of the 114.
That means
P + 5 = 38, or P = 33
Q + 7 = 38, or Q = 31
R - 12 = 38 or R = 50
So, original number of tins in P, Q and R cartons is 33, 31 and 50.
2007-07-11 04:59:13 · answer #2 · answered by Swamy 7 · 0⤊ 0⤋
In P: takes out 25 and put 30. So, it has 5 more tins than original.
In Q: takes out 18 and put 25. So, it has 7 more tins than original.
In R: takes out 30 and put 18. So, it has 12 less tins than original.
After that, the number of tins from every carton is the same.
P + 5 = Q + 7 = R - 12
Then, Q = P - 2 and R = P + 17
P + Q + R = 114
P + ( P - 2 ) + ( P + 17 ) = 114
3P + 15 = 114
3P = 99
P = 33 tins
Q = 31 tins
R = 50 tins
2007-07-11 04:38:13 · answer #3 · answered by Lain Lain 3 · 0⤊ 0⤋
114 / 3 = 38 in each tin. tin p -25 equals 13 + 30=33, q 38+25 equals 63 and r minus 30 = 8. so p has 33, q has 63 and r has 8. all started with 38.
think thats rite
2007-07-11 04:38:51 · answer #4 · answered by Jacklinho 1 · 0⤊ 0⤋
P+Q+R=114
P-25+30=Q+25-18=R-30+18
So, P+5=Q+7=R-12
We can work it out with using P+5 and R-30 first...
R-12=P+5
P=R-17
Then, since Q+7=R-12
R-12=Q+7
Q=R-19
Substitute in equation: R+R-17+R-19=114
3R= 150
R= 50
from the previous equations, we get Q and P:
Q=50-19=31
P= 50-17=33
To check: 50+33+31=114
That is assuming that it is from Q to R and not from Q and R to P... I just got puzzled by the question.
This was edited... I left out a detail in my first one... silly me.
Hope that helped you.
2007-07-11 04:41:46 · answer #5 · answered by Anjo 2 · 0⤊ 0⤋
no need to answer
2007-07-11 04:48:45 · answer #6 · answered by kwijibodavid 1 · 0⤊ 1⤋