SOLUTION: In one multivitamin pill, the ratio of the number of units of Vitamin C to the number of units Vitamin E is 40 to 13. If the pill contains 200 units of Vitamin C, how many units of

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Question 76430: In one multivitamin pill, the ratio of the number of units of Vitamin C to the number of units Vitamin E is 40 to 13. If the pill contains 200 units of Vitamin C, how many units of Vitamin E does it contain?
? units
Answer by wodkit02(9) About Me  (Show Source):
You can put this solution on YOUR website!
To solve this problem, you need to set up a proportion. To do that, we need to look at cooresponding parts in the problem.
%28vitamin+C%29%2F%28vitamin+E%29 = %28vitamin+C+%28in+bottle%29%29%2F%28vitamin+E+%28in+bottle%29%29
Notice how vitamin C is in the numerator in both ratios and vitamin E is in the denominator of both. We place all the variables in that way so their LABELS will cancel out when we multiply.
We know that when the amount of vitamin C = 40 units, the amount of vitamin E = 13 units; thus our first ratio is:
%28vitamin++C%29%2F%28vitamin++E%29 = %2840++units%29%2F%2813++units%29
The second ratio has an unknown in it, because we do not know how many units of vitamin E there are:
%28vitamin++C+%28in++bottle%29%29%2F%28vitamin++E+%28in++bottle%29%29 = %28200++units++vit++C%29%2F%28x%29
We will now set up both ratios equal to each other to solve for x:
%2840++units++vit++C%29%2F%2813++units++vit++E%29 = %28200++units++vit++C%29%2F%28x%29
We cross multiply to get:
40 units vit C * x = 13 units vit C * 200 units vit E
40x (units vit C)(units vit E) = 2600 (units vit C)(units vit E) ....Notice the labels are also muliplied; this will give us the units of our answer
We want x by itself, so we divide each side by 40, as well as by the units vit C label to get:
x = 65 units vit E
Thus a bottle with 200 units of vitamin C will have 65 units of vitamin E.