Ration Question: £150 is divided into the ratio of 4x+10:2x+5:5x+3 How do I find the three amounts?
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blamocur
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I am not sure I understand the problem statement -- can you please post the problem verbatim, as it is stated in your book or lectures?
If It means what I think it means my first question would be : what is the total amount in terms of 'x' ?
If It means what I think it means my first question would be : what is the total amount in terms of 'x' ?
lev888
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Could you post the complete problem statement?
Do you know what it means when we say an amount is divided in a certain ratio?
topsquark
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So it looks like the three parts add to 1:
1 = (4x + 10) + (2x + 5) + (5x + 3)
What's x?
-Dan
BigBeachBanana
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Not necessary
BigBeachBanana
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Can you answer the question in post #2: what is the total amount in terms of 'x' ?
BigBeachBanana
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Did you quote the entire question? It's not possible to know the exact values of each since the ratios are dependent on x.
lev888
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The reason I asked for the complete problem statement is that I don't think we have enough information to solve the problem.
Depending on x there are many possible ratios and therefore ways to divide the total.
E.g. you have $30 and you need to divide it into 2 parts in the ratio of x : x+1.
If x is 1, the ratio is 1:2, the answer is $10 and $20.
If x is 2, the ratio is 2:3, the answer is $12 and $18.
Etc.
If the 3 ratio expressions were a bit different, we would not need to know x to solve it. E.g. 2x+5 : 4x+10 : 6x+15. Do you know why?
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They add up to one whole thing; that is, they sum to 100% of the hundred fifty pounds.
How did you arrive at this summation? What was your reasoning?
a) What do you get, if you sum the expressions for the three "parts" of the hundred fifty? (Hint: Add, and simplify)
b) Since this sum is equal to the hundred fifty, what is the value of x? (Hint: Set up and solve the linear equation.)
c) Then what is the value of each "part"? (Hint: Plug the solution value into each of the three expressions.)
lev888
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Could you clarify this? Not sure where this property comes from. Please see my example with $30 divided per x : x+1 ratio.
Hint:
(4x+10) + (2x+5) + (5x+3) = 150
x = ? ( discussed in response #12) ........ Are there any other possible equation (hence any other possible value of x)
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BigBeachBanana
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This is not true. We're talking about ratios here.
Okay .... more work
(4x+10) * N + (2x+5) * N + (5x+3) * N = 150..............................where N is an integer and possibly a factor of 150 .......... (1,2,3,5,6,.....)......for N = 1 that equatin is correct.
lev888
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Why is N an integer?
Dr.Peterson
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Just to show the issue here, suppose x=1. Then the ratio is 14:7:8, and we could find the three parts.
But if x=2, then the ratio is 18:9:13, and we could again find the parts, but they would be different.
And if x=1.5, then the ratio is 16:8:10.5 = 32:16:21.
The three terms don't have to add up to 1, or to 150; they can be anything.
So unless there is some additional information, we don't know what x is, and therefore can't answer the question numerically.
We can, of course give answers in terms of x, as has been done; but that doesn't appear to be what is being asked.
This is an assumption - trying to "investigate" possible solutions. We can see if N= 1 , we have one possible solution.
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Any time you are adding parts of a thing, summing to the whole thing (whatever that "thing" might be), it may be possible to equate the sum of the parts to 1. (I haven't checked to see if that would be helpful in this particular context.)
...which is why I proposed summing the expressions for the three parts, and setting the result equal to the intended sum. Then one *can* solve for the value of [imath]x[/imath], and can then find the sizes of each of the three parts.
Going out on a limb... because that's the only way it works nicely...? ?