Question

Alice changes size several times. The ratio of her orginal height to her second height is 24 to 5. The ratio of her second height ot he rthird height is 1 to 12. The ratio of her orginal height to her fourth height is 16 to 1. The tallest of these four heights is 10 feet. What is her shortest height?

Answer 1

3 inches

Explanation:

Let's call the heights H1 - H4

Here, we have

H1/H2 = 24/5

H2/H3 = 1/12

And so, we have

H1/H3 = 2/5

Finally

H1/H4 = 16/1.

Thus if H3 = 10 feet, H1 = 4 feet

And from that,

H2 = 1/12 (10 feet) = 5/6 feet = 10 inches

And last,

H4 = 1/16(H1) = 1/16(4 feet) = 1/4 foot = 3 inches

Answer 2

3 inches

Explanation:

Let's call the heights H1 thru H4.

So we have

H1/H2 = 24/5

H2/H3 = 1/12

Therefore if we multiply these, we have

H1/H3 = 2/5

Finally we are given

H1/H4 = 16/1.

By logic we can see that H3 is the tallest.

Thus if H3 = 10 feet, H1 = 4 feet

And from that,

H2 = 1/12 (10 feet) = 5/6 feet = 10 inches

and finally

H4 = 1/16(H1) = 1/16(4 feet) = 1/4 foot =

3 inches