Question

two parts of 21 in such a way that 10 times one of them exceed 9 time the other by 1 are​

Answer 1

Answer:

11 and 10

Step-by-step explanation:

Considering the provided information in the given question, we have :

• Two parts of 21 in such a way that 10 times one of them exceeds 9 times the other by 1.

We are asked to calculate the parts. Let us assume the first part as x and the second part as y.

― According to the question, 21 has been split into two parts. So, the sum of two parts will be 21. Writing this statement in the form of an equation,

$\longrightarrow \sf{\quad {x + y = 21 }}$

From this equation,

$\longrightarrow \sf{\quad {x = 21 - y \quad \dots \bf{(1)} }}$

― Also, these parts of 21 in such a way that 10 times one of them exceeds 9 times the other by 1 .Writing this statement in the form of an equation,

$\longrightarrow \sf{\quad {10x = 9y + 1}}$

Substitute the value of x from the equation (1) in this equation.

$\longrightarrow \sf{\quad {10(21-y) = 9y + 1}}$

Performing multiplication in L.H.S.

$\longrightarrow \sf{\quad {210 - 10y = 9y + 1}}$

Transposing the like terms.

$\longrightarrow \sf{\quad {210 - 1 = 9y + 10y}}$

Performing addition in R.H.S and subtraction in L.H.S.

$\longrightarrow \sf{\quad {209 = 19y}}$

Transposing 19 from RHS to LHS.

$\longrightarrow \sf{\quad { \cancel{\dfrac{209 }{19}}= y}}$

Dividing 209 by 19.

$\longrightarrow \quad \underline{ \boxed{ \textbf{\textsf{11 = y}}}}$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

Now, substitute the value of y in the equation (1) to calculate the value of x.

$\longrightarrow \sf{\quad {x = 21 - y }}$

Substituting the value of y.

$\longrightarrow \sf{\quad {x = 21 - 11 }}$

Performing subtraction.

$\longrightarrow \quad \underline{ \boxed{ \textbf{\textsf{x = 10}}}}$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

Therefore,

⠀⠀⠀★ $\textbf{\textsf{First \; Part \; (x) = 10}}$

⠀⠀⠀★ $\textbf{\textsf{Second \; Part \; (y) = 11}}$