There are two numbers whose sum is 64. the larger number subtracted from 4 times the smaller number gives 31. find the numbers.

There are two numbers whose sum is 64. The larger number subtracted from 4 times the smaller number gives 31. Then the numbers are 45 and 19

Given that, There are two numbers whose sum is 64.  

Let the number be a and b in which a is bigger.

Then, a + b = 64 eqn (1)

The larger number subtracted from 4 times the smaller number gives 31.  

4 x b – a = 31  

4b – a = 31 eqn (2)

We have to find the numbers.

So, from eqn (2)

a = 4b – 31

Subatitute a in (1)

4b – 31 + b = 64

On solving we get

5b  = 64 + 31  

5b = 95

b = 19

So, b = 19, then eqn 1

a + 19 = 64

On simplification,

a = 64 – 19

a = 45  

Hence, the two numbers are 45 and 19

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step-by-step explanation:

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