if the ratio of a to b is 3:4 and the ratio of c to b is 9 to 10, then what is the ratio of a to c?

Question

how do you solve this?
i never learned how....

Answer 1

a : b = 3 : 4
b : c = 10 : 9

multiply 3 and 4 with 10 and 10 and 9 with 4
a : b = 30 : 40
b : c = 40 : 36
therefore a : c = 30 : 36
a : c = 5 :6

Answer 2

These are the ratios:
a:b is 3:4
c:b is 9:10

Since c is 9/10 of b, let's assume that b is 4
at b=4, c=3.6

but if b=4 the first ratio remains true, therefore:
a:c is a ratio of 3:3.6
multiply by 10 and divide by 6

a:c is 5/6

and that's it

Answer 3

I'm not sure but I think the ratio of C to A is 3:3.333333333333333333333333333333333333

Answer 4

A/B=3/4 so 3B=4A or A=3/4B
C/B=9/10 so 9B=10C or C=9/10B
A/C=(3/4B)/(9/10B)
cancel out the Bs and simplify the fraction division to get
A/C=5/6 or 5:6

Answer 5

Ok: a:b = 3:4, so 4a = 3b, and b = 4/3(a).
c:b = 9:10, so 10c = 9b. Substitute for b, then
10c = 9*4/3(a) = 12a. We can simplify by dividing by 2, and
5c = 6a. a/c = 5/6 so a:c = 5:6.

Answer 6

a/b = 3/4
c/b = 9/10
a/b = 1.5/2
= 7.5/10
a/c = 7.5/9
= 15/18
= 5/6
= 5:6