vikkimba17 wrote:A certain compound X has a ratio of 2 oxygen for every 5 carbon. Another
compound Y has a ratio of 1 oxygen for every 4 carbon. If a mixture of X and
Y has a ratio of 3 oxygen for every 10 carbon, what is the ratio of compound
X to compound Y in the mixture?
A)1 to 10
B)1 to 3
C)1 to 2
D)2 to 5
E)2 to 3
The following approach is called ALLIGATION.
Step 1: Convert the ratios to FRACTIONS.
X:
Since oxygen:carbon = 2:5, and 2+5=7, oxygen/total = 2/7.
Y:
Since oxygen:carbon = 1:4, and 1+4=5, oxygen/total = 1/5.
M:
Since oxygen:carbon = 3:10, and 3+10=13, oxygen/total= 3/13.
Step 2: Put the fractions over a COMMON DENOMINATOR.
X = 2/7 = (2*5*13)/(5*7*13) = 130/(5*7*13).
Y = 1/5 = (1*7*13)/(5*7*13) = 91/(5*7*13).
Mixture = 3/13 = (3*5*7)/(5*7*13) = 105/(5*7*13).
Step 3: Plot the 3 numerators on a number line, with the numerators for X and Y on the ends and the numerator for the mixture in the middle.
X 130-----------105-----------91 Y
Step 4: Calculate the distances between the numerators.
X 130-----
25-----105-----
14-----91 Y
Step 5: Determine the ratio in the mixture.
The ratio of X to Y in the mixture is the RECIPROCAL of the distances in red.
X/Y = 14/25.
The required ratio is not among the answer choices.
Feel free to ignore this problem.
More practice will alligation:
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