How to solve (x)/(4)+(y)/(5)+1=23 (x)/(5)+(y)/(4)=23

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Let us know how to solve this question (x)/(4)+(y)/(5)+1=23 (x)/(5)+(y)/(4)=23.

First write the question on the page of the notebook.

(x)/(4)+(y)/(5)+1=23 (x)/(5)+(y)/(4)=23

To solve this question, we will write this question in the simplest form as follows and simplify it.

\displaystyle \frac{x}{4}+\frac{y}{5}+\mathbf{1}=\mathbf{23}\text{ }……….\text{eq(1)}

\displaystyle \frac{x}{5}+\frac{y}{4}=\mathbf{23}………..eq(2)

solve its eq. (1)

\displaystyle \frac{{x\times 5}}{{4\times 5}}+\frac{{y\times 4}}{{5\times 4}}+\mathbf{1}=\mathbf{23}\text{ }

\displaystyle \frac{{5x}}{{20}}+\frac{{4y}}{{20}}+\mathbf{1}=\mathbf{23}\text{ }

\displaystyle \frac{{5x+4y}}{{20}}=\mathbf{23}\text{ -}\mathbf{1}

\displaystyle \frac{{5x+4y}}{{20}}=22

\displaystyle 5x+4y=22\times 20

\displaystyle 5x+4y=440……..eq(3)

there fore ,

\displaystyle \frac{{4x}}{{20}}+\frac{{5y}}{{20}}=\mathbf{23}

\displaystyle 4x+5y=\mathbf{23}\times 20

\displaystyle 4x+5y=460…….eq(4)

Multiplying by 4 in Equation.(3)

\displaystyle 20x+16y=1760……..eq(5)

Multiplying by 5 in Equation.(4)

\displaystyle 20x+25y=2300…….eq(6)

Subtracting equation (5) from equation.(6)

\displaystyle \left( {20x+25y} \right)-\left( {20x+16y} \right)=2300-1760

\displaystyle 20x+25y-20x-16y=2300-1760

\displaystyle 20x-20x+25y-16y=2300-1760

\displaystyle \cancel{{20x}}-\cancel{{20x}}+25y-16y=2300-1760

\displaystyle 25y-16y=2300-1760

\displaystyle 9y=540

\displaystyle y=\frac{{540}}{9}

\displaystyle y=60……………….eq(7)

Putting y=60 in eqution (1),

\displaystyle \frac{x}{4}+\frac{y}{5}+1=23\text{ }

\displaystyle \frac{x}{4}+\frac{{60}}{5}+1=23\text{ }

\displaystyle \frac{x}{4}+12+1=23\text{ }

\displaystyle \frac{x}{4}+13=23\text{ }

\displaystyle \frac{x}{4}=23\text{ -13}

\displaystyle \frac{x}{4}=10

\displaystyle x=40

Thus the ultimate solution of this article is,

x=40 and y=60 [Answer]

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