Question

The sum of two number is 80 and if the larger number exceed 4 times the smaller by 5.
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Answer 1

$\huge\sf\pink{Answer}$

☞ The Numbers are 65 and 15

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$\huge\sf\blue{Given}$

✭ Sum of 2 Numbers is 80

✭ Larger Number exceeds 4 times the smaller by 5

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$\huge\sf\gray{To \:Find}$

◈ The Numbers?

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$\huge\sf\purple{Steps}$

Let the larger number be x and the smaller one be y 

$\bullet\:\underline{\textsf{ As Per the Question}}$

➳ $\sf x+y=80\quad -eq(1)$

➳ $\sf x=4y+5$

➳ $\sf x-4y=5\quad -eq(2)$

Subtracting eq(2) from eq(1), we get  

➝ $\sf 5y=75$  

➝ $\sf y = \dfrac{75}{5}$

➝ $\sf\red{y=15}$

Putting value of y in eq(1)

»» $\sf x + y = 80$

»» $\sf x+15=80$

»» $\sf x = 80 - 15$

»» $\sf\orange{x = 65}$

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Answer 2

Let , the two numbers are x and y , x > y

Given ,

The sum of two number is 180

x + y = 80 --- (i)

The larger number exceed 4 times the smaller by 5

x - 4y = 5 --- (ii)

Subtract eq (ii) from eq (i) , we get

x + y - (x - 4y) = 80 - 5

5y = 75

y = 15

Put the value of y = 15 in eq (i) , we get

x + 15 = 80

x = 65

$\therefore\sf \underline{The \: two \: numbers \: are \: 65 \: and \: 15}$