SOLUTION: a:b=2:5 and a:c=3:7. What is c:b? A. 5:7 B. 14:15 C. 2:7 D. 15:14 E. 7:5

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Question 1183921: a:b=2:5 and a:c=3:7. What is c:b?
A. 5:7
B. 14:15
C. 2:7
D. 15:14
E. 7:5
Found 5 solutions by MathLover1, Edwin McCravy, greenestamps, ikleyn, josgarithmetic:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

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What is ?



or


answer: B.


Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
a:b=2:5 and a:c=3:7. What is c:b?
Product of the means equals the product of the extremes:

5a = 2b and 7a = 3c



Dividing equals by equals:







Cross-multiply:



 Make c and 15 the extremes, and 14 and b the means:



Edwin
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


I would solve this problem by a very different method from the similar ones used by the other two tutors; I have a particular dislike for that "product of the means equals product of the extremes" rule, since it introduces unneeded new vocabulary.

Given the ratio of a:b and the ratio of a:c, and needing to find the ratio c:b, I would rewrite the second ratio as c:a; then I would "eliminate the middle man" in the ratios c:a and a:b.

c:a = 7:3
a:b = 2:5

rewrite each ratio as an equivalent ratio using the same number for a in both:

c:a = 14:6
a:b = 6:15

Combine them into a ratio comparing all three numbers...

c:a:b = 14:6:15

and eliminate the middle man:

c:a = 14:15
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

Of the three methods,  shown by three tutors,  no one is better than another.


They all are good and are  EQUIVALENT,  and you,  the visitor,  can use  ANY  of them, with the same success.


It would be nice  (profitable)  for you to know all three methods.


Good student should know all of them - - - it is a necessary condition to have peace in mind and to be happy (!)



Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
a     b    c           multiply by       a     b     c
2     5                         3        6    15
3         7                     2        6           14

The empty cells in the second part now unnecessary and the ratio a:b:c is 6:15:14.
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