Question

A vessel is full of a mixture of kerosene and petrol in which there is 18% kerosene.Eight litres are drawn off and then the vessel is filled with petrol.If the kerosene is now 15% how much does the vessel hold?

Answer 1

a.40
b.36
c.48
d.32

Answer 2

@freckles

Answer 3

@amistre64

Answer 4

how much what does it hold? total volume?

Answer 5

total litres it can have

Answer 6

lets develope some inital conditions

Answer 7

k + p = n

k/(k+p) = .18
p/(k+p) = .82

subtract 8 and add in some L

k/(k+p-8+L) = .15
p/(k+p-8+L) = .85

Answer 8

ok

how to proceed now

Answer 9

substitution comes to mind

Answer 10

k/(k+p) = .18

k = .18k + .18p
.82k =.18p

k = 18/82 p

which reduces this to equations of p and L

Answer 11

ok

so how to proceed ,i cant get the way

Answer 12

we know:

k/(k+p-8+L) = .15
p/(k+p-8+L) = .85

and we know k = 9/41 p

Answer 13

multiply acorss, and combine like terms, then you are set for a system of 2 equations in 2 unknowns that will hopefully give us a solution :)

Answer 14

m stii confused

whick term to multiply with which term

Answer 15

k/(k+p-8+L) = .15

p/(k+p-8+L) = .85

substitute for k ... show me some work

Answer 16

9/[41p(k+p-8+L)] = .15


p/(k+p-8+L) = .85

do i have to multiply this to cancel p

Answer 17

k/(k+p-8+L) = .15
p/(k+p-8+L) = .85


k = .15(k+p-8+L)
p = .85(k+p-8+L)

k = .15k +.15p -8(.15) + .15L
p = .85k + .85p -8(.85) +.85L


9/41 p = .15(9/41 p) +.15p -8(.15) + .15L
p = .85(9/41 p) + .85p -8(.85) +.85L


0 = p(.15(9/41) + .15 - 9/41) -8(.15) + .15L
0 = .85(9/41 p) + .85p - p -8(.85) +.85L


0 = p(.15(9/41) + .15 - 9/41) -8(.15) + .15L
0 = p(.85(9/41) + .85 - 1) -8(.85) +.85L


8(.15) = p (.15(9/41) + .15 - 9/41) + .15L
8(.85) = p (.85(9/41) + .85 - 1) +.85L

Answer 18

8(.15) = -3/82 p + .15L
8(.85) = 3/82 p + .85L

hmmm it seems to reduce so that it eliminates p from the getgo

Answer 19

im gonna have to make sure i kept things in order

Answer 20

A vessel is full of a mixture of kerosene and petrol

k+p = n

in which there is 18% kerosene.

k/(k+p) = .18 and the rest is p lol
p/(k+p) = .82

k/.18 = (k+p) = p/.82


Eight litres are drawn off and then the vessel is filled with petrol.

new amount: k+p-8+Lp that might be better

Answer 21

so the new ratios are:

k/(k+p-8+Lp) = .15
p/(k+p-8+Lp) = .85

Answer 22

we can substitute one of the variables, p or k, and possible (k+p)

Answer 23

k/.18 = (k+p) = p/.82

k+p = p/.82
k = 9/41 p


k = .15(k+p-8+Lp)
p = .85(k+p-8+Lp)


9/41 p = .15(p/.82-8+Lp)
p = .85(p/.82-8+Lp)

Answer 24

i still dont get