Question

If a varies directly as b, and a = 28 when b = 7, find b when a = 5.

Answer 1

If a varies directly as b:
a = k b
28 = 7 k
k = 28 : 7 = 4
When a = 5:
5 = 4 b
b = 5 : 4
b = 1.25

Answer 2

Answer:

Value of b = $\frac{5}{4}$ =1.25.

Step-by-step explanation:

Direct Variation states that a relationship  between two variables in which one is a constant multiple of the other.

*if one variable changes the other changes in proportion to the first.

*If a is directly proportional to b i.e,  

$a \propto b$ then it is of the form

a = kb     ;where k is constant variation.  

Given: a varies directly as b;

then, by definition of direct variation;

we have;

$a = kb$             .....[1]

Substitute the value of a =28 and b =7 to solve for k;

$28 = k(7)$

Divide both sides by 7 we have;

$\frac{28}{7}=\frac{7k}{7}$

Simplify:

k =4

now, find b using same method when a =5;

then;

after substituting the value of a = 5 and k=4 in [1] ;

$5=(4)b$

Divide by 4 to both sides we get;

$b =\frac{5}{4}$

Therefore, the value of b = $\frac{5}{4}$ =1.25