Algebra :If a: b = 7 : 9 and b : c = 5 : 7, then what is a : c

Question

If a: b = 7 : 9 and b : c = 5 : 7, then what is a : c

(a) 5 : 9 (b) 3 : 5

(c) 7 : 21 (d) 7 : 15

Answer 1

a:b = 7:9

b:c = 5:7

We want to make b the same in both ratios, by finding the LCM of 9 and 5 - which is 45

Without changing the essence of the ratios we can multiply both terms of the first one (a:b = 7:9) by 5; and the second one (b:c = 5:7) by 9

As a result we got

a:b = 35:45

b:c = 45:63

Now we can just combine the ratios by getting rid of b since it's the same

a:c = 35:63, and after simplifying (dividing both terms by 7) the final answer is a:c = 5:9

Answer 2

a/b = 7/9

b/c = 5/7

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a/c = (a/b)*(b/c)

a/c = (7/9)*(5/7)

a/c = (7/9)*(5/7)

a/c = 5/9

a:c is 5:9