# Ex.4.4 Q1 Simple-Equations Solution - NCERT Maths Class 7

## Question

Set up equations and solve them to find the unknown numbers in the following cases:

(a) Add \(4\) to eight times a number; you get \(60\).

(b) One fifth of a number minus \(4\) gives \(3\).

(c) If I take three fourths of a number and add \(3\) to it, I get \(21\).

(d) When I subtracted \(11\) from twice a number, the result was \(15\).

(e) Munna subtracts thrice the number of notebooks he has from \(50\), he finds the result to be \(8\).

(f) Ibenhal thinks of a number. If she adds \(19\) to it and divides the sum by \(5\), she will get \(8\).

(g) Anwar thinks of a number. If he takes away \(7\) from \(\begin{align} \frac{5}{2}\end{align} \) of the number, the result is \(23\).

## Text Solution

**What is Known?**

Statement of the Equation.

**What is unknown?**

Equation and the value of the variable which satisfy the equation.

**Reasoning:**

First read the statement of the question carefully suppose the number as any variable or alphabet then follow the steps given in the question.

**Steps:**

(a) Let the number be *\(x\)*. According to the question,

\[\begin{align} 8x + 4 &= 60\\8x= 60 \,– 4 &= 56 \\ x = \frac{{56}}{8} &= 7\end{align}\]

(b) Let the number be *\(y\)*. According to question,

\[\begin{align}\frac{y}{5} – 4 &=3\\ \frac{y}{5} &= 3 + 4\\ \frac{y}{5} &= 7\\ y&= 35\end{align}\]

(c) Let the number be *\(x\)*. According to question,

\[\begin{align} \frac{3x}{4}+3&=21 \\ \frac{3x}{4}&=21-3 \\ \frac{3x}{4}&=18 \\ x&=\frac{18\times 4}{3} \\ x&=24 \\ \end{align}\]

(d) Let the number be *\(x\)*. According to question,

\[\begin{align}2x- 11 &= 15\\2x &= 15 + 11\\2x &= 26\\ x &= \frac{{26}}{5} = 13\end{align} \]

(e) Let the number be *\(x\)*. According to question,

\[\begin{align} 50 - 3x &= 8\\-3x = 8 \,– 50 &= -42\\x =\frac{{ - 42}}{{ - 3}} &= 14\end{align}\]

(f) Let the number be *\(z\)*. According to question,

\[\begin{align} \frac{z + 19}{5} &= 8\\z + 19 &= 40\\z = 40 \,– 19 &= 21\end{align} \]

(g) Let the number be *\(x\)*. According to question,

\[\begin{align}& \frac{5x}{2}~7=23~ \\ & ~\frac{5x}{2}=23+7~ \\ & \frac{5x}{2}~=30 \\ \end{align}\]

\[\begin{align}x = 30 \times \frac{2}{5} = 12\end{align}\]

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