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Question 1017845: the ratio of money with jane and sarah is 4:5 and that with sarah and margaret is 5:6. if jane has 280, then what is the amount of money margaret has?
Found 2 solutions by Theo, ankor@dixie-net.com:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = amount of money jane has.
let y = amount of money sarah has.
let z = amount of money margaret has.
the ratio of money that jane has to what sarah has is given by the equation x/y = 4/5.
the ratio of money that sarah has to what margaret has is given by the equation y/z = 5/6.
you have two equations so far.
x/y = 4/5 and y/z = 5/6.
in the first equation, you can solve for x to get:
x = 4/5 * y.
in the second equation, you can solve for y to get y = 5/6 * z.
you have:
x = 4/5 * y and y = 5/6 * z.
since y = 5/6 * z, you can replace y in the equation of x = 4/5 * y with 5/6 * z to get:
x = 4/5 * y becomes x = 4/5 * (5/6 * z).
simplify this equation to get x = 20/30 * z which becomes x = 2/3 * z.
you are given that x = 280.
since x = 2/3 * z, then 280 = 2/3 * z.
solve for z to get z = 3/2 * 280 = 3 * 140 = 420.
if this was done correctly, than margaret must have 420 dollars.
let's see if this is true.
we know that jane has 280 dollars.
we know that the ratio between the money that jane has and the money that sarah has is 4/5.
this means that 280/y = 4/5
solve for y to get y = 5/4 * 280 = 5 * 70 = 350 dollars.
we now know that sarah has 350 dollars.
we know that the ratio between what sarah has and margaret has is 5/6.
this means that 350/z = 5/6
solve for z to get z = 6/5 * 350 = 6 * 70 = 420 dollars.
looks good.
margaret must have 420 dollars and sarah must have 350 dollars.
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since you were only asked to find the value of money that margaret has, then your solution is 420 dollars.
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we now know that jane has 280 and sara has 350 and margaret has 420.
jane/sara = 280/350 = 28/35 = 4/5.
sara/margaret = 350/420 = 35/42 = 5/6.
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! the ratio of money with Jane and Sarah is 4:5
:
let x = the first multiplier
then
4x = amt that Jane has
5x = amt that Sarah has
:
:
"that with Sarah and Margaret is 5:6."
let y = the second multiplier
then
5y = amt Sarah has
6y = amt Margaret has
:
From this we know that 5x = 5y, therefore x = y
:
if Jane has 280, then what is the amount of money Margaret has?
4x = 280
x = 70 is the multiplier
therefore
6*70 = $420 is the amt Margaret has
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