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

Algebra ->  Expressions-with-variables -> 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      Log On


   

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) About Me  (Show Source):
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a%3Ab=2%3A5 =>a=2b%2F5
a%3Ac=3%3A7=>a=3c%2F7
What is c%3Ab?
2b%2F5=3c%2F7
14b=15c
14%2F15=c%2Fb
or
c%3Ab=14%3A15

answer: B. 14%3A15


Answer by Edwin McCravy(20056) About Me  (Show Source):
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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

system%285a=2b%2C7a=3c%29

Dividing equals by equals:

%285a%29%2F%287a%29=%282b%29%2F%283c%29

%285cross%28a%29%29%2F%287cross%28a%29%29=%282b%29%2F%283c%29

5%2F7=%282b%29%2F%283c%29

Cross-multiply:

15c=14b

c%2A15=b%2A14 Make c and 15 the extremes, and 14 and b the means:

c%3Ab=14%3A15

Edwin

Answer by greenestamps(13200) About Me  (Show Source):
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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) About Me  (Show Source):
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.

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) About Me  (Show Source):
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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.