Ratio: Amanda, Beatrix and Cathy received the same sum of money, S each year...

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mariss

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In 2013 and in 2014, Amanda, Beatrix and Cathy received the same sum of money, S each year, for their work on a project.

In 2013, Amanda, Beatrix and Cathy divided the sum received in the ratio 8: 7: 5 whilst in 2014, they divided the sum received in the ratio 7: 5: 4

In 2014 Amanda received €240 more than in 2013.

Work out the total sum of money the three women received each year.



I tried to worked it out by saying that:
In 2013: 8 + 7 + 5 = 20 therefore Amanda received x/20 X 8
In 2014: 7 + 5 + 4 = 16 Therefore Amanda received [x + (240*3)]/16 X 7 I did 240*3 because if Amanda received €240 more, the others should received €240 more as well. I ended it up with a negative number which is obviously incorrect.
Can anyone help me please?In 2013 and in 2014, Amanda, Beatrix and Cathy received the same sum of money, S each year, for their work on a project.

In 2013, Amanda, Beatrix and Cathy divided the sum received in the ratio 8: 7: 5 whilst in 2014, they divided the sum received in the ratio 7: 5: 4

In 2014 Amanda received €240 more than in 2013.

Work out the total sum of money the three women received each year.



I tried to worked it out by saying that:
In 2013: 8 + 7 + 5 = 20 therefore Amanda received x/20 X 8
In 2014: 7 + 5 + 4 = 16 Therefore Amanda received [x + (240*3)]/16 X 7 I did 240*3 because if Amanda received €240 more, the others should received €240 more as well. I ended it up with a negative number which is obviously incorrect.
Can anyone help me please?
 
mariss said:
In 2013 and in 2014, Amanda, Beatrix and Cathy received the same sum of money, S each year, for their work on a project.

In 2013, Amanda, Beatrix and Cathy divided the sum received in the ratio 8: 7: 5 whilst in 2014, they divided the sum received in the ratio 7: 5: 4

In 2014 Amanda received €240 more than in 2013.

Work out the total sum of money the three women received each year.



I tried to worked it out by saying that:
In 2013: 8 + 7 + 5 = 20 therefore Amanda received x/20 X 8
In 2014: 7 + 5 + 4 = 16 Therefore Amanda received [x + (240*3)]/16 X 7 I did 240*3 because if Amanda received €240 more, the others should received €240 more as well. I ended it up with a negative number which is obviously incorrect.
Can anyone help me please?In 2013 and in 2014, Amanda, Beatrix and Cathy received the same sum of money, S each year, for their work on a project.

In 2013, Amanda, Beatrix and Cathy divided the sum received in the ratio 8: 7: 5 whilst in 2014, they divided the sum received in the ratio 7: 5: 4

In 2014 Amanda received €240 more than in 2013.

Work out the total sum of money the three women received each year.



I tried to worked it out by saying that:
In 2013: 8 + 7 + 5 = 20 therefore Amanda received x/20 X 8
In 2014: 7 + 5 + 4 = 16 Therefore Amanda received [x + (240*3)]/16 X 7 I did 240*3 because if Amanda received €240 more, the others should received €240 more as well. I ended it up with a negative number which is obviously incorrect.
Can anyone help me please?
Click to expand...
A, B and C received €S in 2013. So A received S/20 * 8, not x/20 X 8-unless of course YOU know that YOUR x is the same as S. Of course no one reading your post will know that. That is, PLEASE define YOUR variables.

In 2014 A, B and C received €S. This time A received S/16*7

In 2014 Amanda received €240 more than in 2013

So S/16*7 - S/20 * 8 = 240. Solve for S. Continue from here.
 
mariss said:
In 2013 and in 2014, Amanda, Beatrix and Cathy received the same sum of money, S each year, for their work on a project.

In 2013, Amanda, Beatrix and Cathy divided the sum received in the ratio 8: 7: 5 whilst in 2014, they divided the sum received in the ratio 7: 5: 4

In 2014 Amanda received €240 more than in 2013.

Work out the total sum of money the three women received each year.



I tried to worked it out by saying that:
In 2013: 8 + 7 + 5 = 20 therefore Amanda received x/20 X 8
In 2014: 7 + 5 + 4 = 16 Therefore Amanda received [x + (240*3)]/16 X 7 I did 240*3 because if Amanda received €240 more, the others should received €240 more as well. I ended it up with a negative number which is obviously incorrect.
Can anyone help me please?In 2013 and in 2014, Amanda, Beatrix and Cathy received the same SUM of money, S each year, for their work on a project.

In 2013, Amanda, Beatrix and Cathy divided the SUM received in the ratio 8: 7: 5 whilst in 2014, they divided the SUM received in the ratio 7: 5: 4

In 2014 Amanda received €240 more than in 2013.

Work out the total SUM of money the three women received each year.



I tried to worked it out by saying that:
In 2013: 8 + 7 + 5 = 20 therefore Amanda received x/20 X 8
In 2014: 7 + 5 + 4 = 16 Therefore Amanda received [x + (240*3)]/16 X 7 I did 240*3 because if Amanda received €240 more, the others should received €240 more as well. I ended it up with a negative number which is obviously incorrect.
Can anyone help me please?
Click to expand...

What does that mean?

Are these SUMs referring to the same amount of money?
 
Thank you. I managed to find the sum S which is €6400. Then I worked out the money received by each person in each year and I added them. Thanks a lot :).
 
mariss said:
Thank you. I managed to find the sum S which is €6400. Then I worked out the money received by each person in each year and I added them. Thanks a lot :).
Click to expand...
Can you please say why you keep saying the sum S? Personally I did not get S=6400.
 
Subhotosh's point is that "In 2013 and in 2014, Amanda, Beatrix and Cathy received the same sum of money, S each year, for their work on a project." could mean that in 2013, The amount of money each Amanda, Beatrix, and Cathy received was the same- and the same in 2014 but that that amount was different in each year. Or it could mean that in 2013, Amanda, Beatrix, and Cathy, received different amounts of money but that they each received, in 2014, the same amount that they each received in 2013.
 
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