Question

The difference of two numbers is 3 and the sum of the tthree times and the larger one and the twice and smaller one and twice the smaller is 19. find he two number

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given two numbers whose difference is 3
• Sum of three the larger number and twice the smaller number is 19

To Find:

• We have to find both the numbers

Solution:

Let greater number = x

Smaller number = y

We have been given that

$\large\boxed{\sf{\pink{ x - y = 3 }}}$

$\implies \sf{x = y + 3 }$

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$\underline{\large\mathfrak\orange{According \: to \: the \: Question}}$

Sum of three the larger number and twice the smaller number is 19

$\implies \large\boxed{\sf{\green{ 3x + 2y = 19}}}$

Putting value of x = ( y + 3 )

$\implies \sf{ 3 \: (y+3)+ 2y = 19}$

$\implies \sf{ 3y + 9 + 2y = 19}$

$\implies \sf{ 5y = 19 - 9}$

$\implies \sf{ 5y = 10}$

$\implies \sf{ y = \dfrac{10}{5}}$

$\implies \sf{ y = 2 }$

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$\underline{\large\mathfrak\orange{Finding \: the \: Values}}$

Putting y = 2

$\implies \sf{ x = 2 + 3 }$

$\implies \sf{ x = 5 }$

$\implies \boxed{\sf{ x = 5 }}$

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$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{\red{Greater \: Number = 5}}}$

$\large\boxed{\sf{\purple{Smaller \: Number = 2}}}$

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$\huge\mathfrak\green{Verification:}$

1 ) Difference of Numbers

$\hookrightarrow \boxed{ \sf{ Difference = 5 - 2 = 3 }}$

2 ) Sum of three the larger number and twice the smaller number is 19

$\hookrightarrow \sf{ Sum = 3 \times 5 + 2 \times 2}$

$\hookrightarrow \sf{ Sum = 15 + 4}$

$\hookrightarrow \boxed{\sf{ Sum = 19} }$

Hence Verified !!!