SOLUTION: We need help. My daughter has been working on this problem all weekend and we still do not get the right answer. We are working on inverse variation as a ratio. The problem is :

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Question 84355This question is from textbook Algebra 2 An incremental Development
: We need help. My daughter has been working on this problem all weekend and we still do not get the right answer. We are working on inverse variation as a ratio. The problem is : The ratio of acrobats in blue to acrobats in pink was 4 to 5. Those who wore blue numbered 1200 fewer than twice the number who wore pink. How many wore blue, and how many wore pink? All help is appreciated. Thank you! This question is from textbook Algebra 2 An incremental Development

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
First, let B represent the number of acrobats wearing blue. Also let P represent the number
of acrobats wearing pink.
.
Two times the number of acrobats wearing pink is, therefore, 2*P
.
1200 less that that is 2*P - 1200 and that is equal to the number of acrobats wearing
blue. So we can write that B = 2*P - 1200
.
So we can write the ratio of blue to pink acrobats as:
.
B%2FP+=+%282%2AP-1200%29%2FP
.
But you were told in the problem that B%2FP+=+4%2F5. Substitute this into the ratio
equation to get:
.
4%2F5+=+%282%2AP+-1200%29%2FP
.
An easy way to work on this proportion (a fraction on the opposite sides of the equal sign)
is to cross multiply ... that is multiply the numerator on the left side by the denominator
on the right side and set this product equal to the product you get by multiplying
the numerator on the right side by the denominator on the left side. For this problem
that translates to multiplying 4 by P and setting that equal to multiplying (2*P - 1200)
by 5. This gives you the equation:
.
4%2AP+=+%282%2AP+-+1200%29%2A5
.
Multiply out the right side and the equation becomes:
.
4%2AP+=+10%2AP+-+6000
.
To get the P terms on the same side of the equation subtract 10P from both sides of the
equation. This results in:
.
-6%2AP+=+-6000
.
Solve for P by dividing both sides of the equation by -6 which is the multiplier of P.
When you do this division, the result is:
.
P+=+1000
.
You now know that there are 1000 acrobats in pink. Since the ratio of Blue to Pink is 4 to 5,
you can write:
.
4%2F5+=+B%2F1000
.
Using the cross product process just as before results in:
.
4%2A1000+=+B%2A5
.
Dividing both sides by 5 results in:
.
B+=+%284%2A1000%29%2F5+=+4000%2F5+=+800
.
So there are 800 acrobats dressed in blue and 1000 acrobats dressed in pink.
.
Check ... twice the acrobats dressed in pink is 2000. Notice that the number dressed in
blue is 2000 - 800 = 1200 less than that number. That checks. And the ratio of 800 acrobats
in blue to 1000 in pink is 800%2F1000 and that reduces to 4%2F5 so it also checks.
.
Hope this helps you to see how to work the problem.