A two-digit number is four times the sum of i | vedclass

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(B) Let the two-digit number be represented as $10x + y$,where $x$ is the tens digit and $y$ is the units digit.According to the problem,the number is

Vedclass · Accepted Answer

$24$

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(B) Let the two-digit number be represented as $10x + y$,where $x$ is the tens digit and $y$ is the units digit.According to the problem,the number is four times the sum of its digits:$10x + y = 4(x + y)$$10x + y = 4x + 4y$$6x = 3y$$y = 2x$ (Equation $1$)Also,the number is three times the product of its digits:$10x + y = 3xy$ (Equation $2$)Substitute $y = 2x$ into Equation $2$:$10x + 2x = 3x(2x)$$12x = 6x^2$Since $x$ cannot be $0$ for a two-digit number,we divide by $6x$:$x = 2$Now,find $y$ using Equation $1$:$y = 2(2) = 4$Therefore,the number is $10(2) + 4 = 24$.

$A$ two-digit number is four times the sum of its digits and three times the product of its digits. The number is:

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