Question

In which of the options below will the number 12 correctly fill in the blank? Select all that apply.

A) 3 : 4 = 9 : ___
B) 5 : 6 = 10 : ___
C) 6 : ___ = 1 : 3
D) ___ : 14 = 6 : 7


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A

Answer 1

Let's evaluate each option to see if the number 12 can fill in the blank:

A) 3 : 4 = 9 : ___
We can set up a proportion:
3 / 4 = 9 / x
Cross multiplying gives us:
3x = 36
x = 12
**This option is valid.**

B) 5 : 6 = 10 : ___
Setting up the proportion:
5 / 6 = 10 / x
Cross multiplying gives us:
5x = 60
x = 12
**This option is valid.**

C) 6 : ___ = 1 : 3
Setting up the proportion:
6 / x = 1 / 3
Cross multiplying gives us:
6 * 3 = 1 * x
x = 18
**This option is not valid.**

D) ___ : 14 = 6 : 7
Setting up the proportion:
x / 14 = 6 / 7
Cross multiplying gives us:
7x = 84
x = 12
**This option is valid.**

In summary, the options where the number 12 correctly fills in the blank are:

**A, B, and D.**