Ratio

1) If 1 over a :1 over b:1 over C = 3 : 5 : 4, find a:b:c.

1/a : 1/b : 1/c = 3 : 5 : 4
Let 1/a = 3k, 1/b = 5k and 1/c = 4k
Then a = 1/(3k), b = 1/(5k) and c = 1/(4k)

a : b : c
= 1/(3k) : 1/(5k) : 1/(4k)
= 1/3 : 1/5 : 1/4
= 60 x (1/3) : 60 x (1/5) : 60 x (1/4)
= 20 : 12 : 15


2) The ratio of these integers is 4 : 8 : 7. If the sum of the three integers is 152, find the smallest integer.

Let a, b and c be the three numbers from the smallest to the greatest.

a : b : c = 4 : 8 : 7
Let a = 4k, b = 8k and c = 7k

a + b + c = 152
4k + 8k + 7k = 152
19k = 152
k = 8
4k = 32

The smallest integer = 32

why there has 1/2

1/a：1/b：1/c=3：5：4
=>
a：b：c
=1/2：1/5：1/4
=(20*1/2)：(20*1/5)：(20*1/4)
=10：4：5

1/a:1/b:1/c=3:5:4
Let 1/a=3k,1/b=5k,1/c=4k
a=1/3k,b=1/5k,c=1/4k
So a:b:c=(1/3k):(1/4k):(1/5k)=(1/3):(1/5):(1/4)

a=1over3
b=1over5
c=1over4