Answer
Verified
421.8k+ views
Hint: Here first we assume two variables and write the equations according to the condition given in question and solve the equations to get one of the values of the variable and substitute in the equation to get another variable.
Complete step-by-step answer:
First let us assume the two numbers are x and y
Then according to question, we will be having two equations those are
\[x + y = {\text{2}}7\] …… (1)
\[xy = 182\] …… (2)
Equation 1 can be written as
$\Rightarrow$ \[x = {\text{2}}7 - y\] …… (3)
On putting the value of x in equation (3), we get
$\Rightarrow$ $\left( {27 - y} \right)\left( y \right) = 182$
Above equation can also be written as
$\Rightarrow$ ${y^2} - 27y + 182 = 0$
On splitting we get
$\Rightarrow$ ${y^2} - 13y - 14y + 182 = 0$
$\Rightarrow$ $\left( {y - 13} \right)\left( {y - 14} \right) = 0$
From the equation above either y = 13 or y = 14.
Putting the value of y in equation(1) we get \[x = 14\] when \[y = 13\] and \[x = 13\] when \[y = 14\]
Hence the two numbers are 13 and 14.
Note: In these types of questions first assume the variables and then write the equation according to the condition given in the question then solve the equations to get the value of the variables.Students should take care while assuming the variables and writing the equations according to the question.
Complete step-by-step answer:
First let us assume the two numbers are x and y
Then according to question, we will be having two equations those are
\[x + y = {\text{2}}7\] …… (1)
\[xy = 182\] …… (2)
Equation 1 can be written as
$\Rightarrow$ \[x = {\text{2}}7 - y\] …… (3)
On putting the value of x in equation (3), we get
$\Rightarrow$ $\left( {27 - y} \right)\left( y \right) = 182$
Above equation can also be written as
$\Rightarrow$ ${y^2} - 27y + 182 = 0$
On splitting we get
$\Rightarrow$ ${y^2} - 13y - 14y + 182 = 0$
$\Rightarrow$ $\left( {y - 13} \right)\left( {y - 14} \right) = 0$
From the equation above either y = 13 or y = 14.
Putting the value of y in equation(1) we get \[x = 14\] when \[y = 13\] and \[x = 13\] when \[y = 14\]
Hence the two numbers are 13 and 14.
Note: In these types of questions first assume the variables and then write the equation according to the condition given in the question then solve the equations to get the value of the variables.Students should take care while assuming the variables and writing the equations according to the question.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
State the differences between manure and fertilize class 8 biology CBSE
Why are xylem and phloem called complex tissues aBoth class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
What would happen if plasma membrane ruptures or breaks class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What precautions do you take while observing the nucleus class 11 biology CBSE
What would happen to the life of a cell if there was class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE