In this page ratio and proportion solution10 we are going to see solution of each question from the worksheet ratio and proportion.
(15) If a : b = 3 : 2 and b : c = 5 : 8,find a: c and a : b : c .
Solution:
a : b =3 : 2
a/b = 3/2
b : c = 5/8
b/c = 5/8
we can write a : c as (a/c) => (a/b) x (b/c) = (3/2) x (5/8)
(a/c) = (15/16)
a : c = 15 : 16
a : b =3 : 2
= 1 : (2/3)
Now we have to multiply by 15,
= 1(15) : (2/3) (15) : 16 (15)
= 15 : 10 : 240
We can simplify this by 5,so we get
a : b : c = 3 : 2 : 48
(16) If x : y = 5 : 7 and y : z = 4 : 5, find x : z and x : y : z
Solution:
x : y = 5 : 7
x/y = 5/7
y : z = 4 : 5
y/z = 4/5
we can write x : z as (x/z) => (x/y) x (y/z) = (5/7) x (4/5)
(x/z) = (4/7)
x : z = 4 : 7
y : z = 4 : 5
= 1 : (5/4)
Now we are going to multiply it by 4, so we get
= 4 : (5/4) x 4
= 4 : 5
x : y : z = 4 : 4 : 5
(17) If x : y = 2 : 1 find (5 x + 8y) : (6 x – 7y)
Solution:
x : y = 2 : 1
x/y = 2/1
(5 x + 8y) : (6 x – 7y) = (5 x + 8 y) /(6 x – 7 y)
Divide both numerator and denominator by x, so we get
= [5 + 8(x/y)]/[6 – 7(x/y)]
= [5 + 8(2/1)]/[6 – 7(2/1)]
= [5 + 16]/[6 – 14]
= 21/[– 8]
= -21/8
Therefore the value of (5 x + 8y) : (6 x – 7y)is -21/8
ratio and proportion solution10 ratio and proportion solution10