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castortr0y [4]
3 years ago
12

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

Mathematics
2 answers:
Rufina [12.5K]3 years ago
6 0
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
Jlenok [28]3 years ago
4 0

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



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