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# 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 $\frac{5}{2}$ of the number, the result is 23.

**To do:**

We have to set up equations and solve them to find the unknown numbers in the given cases.

**Solution:**

(a) Let the number be $x$.

According to the question,

$8\times x+4=60$

$8x=60-4$

$8x=56$

$x=\frac{56}{8}$

$x=7$

(b) Let the number be $y$.

According to question,

$\frac{1}{5}(y)-4=3$

$\frac{y}{5}=3+4$

$\frac{y}{5}=7$

$y=7\times5$

$y=35$

(c) Let the number be $x$.

According to question,

$\frac{3}{4}(x)+3=21$

$\frac{3x}{4}=21-3$

$\frac{3x}{4} =18$

$x =18\times \frac{4}{3}$

$x=6\times4$

$x=24$

(d) Let the number be $x$.

According to question,

$2 \times x-11=15$

$2x=15+11$

$2x=26$

$x=\frac{26}{2}$

$x=13$

(e) Let the number of notebooks be $x$.

According to question,

$50-3\times x=8$

$-3x=8 -50$

$-3x=-42$

$x=\frac{-42}{-3}$

$x=14$

(f) Let the number be $x$.

According to question,

$\frac{x+19}{5}=8$

$x+19=8\times5$

$x=40-19$

$x=21$

(g) Let the number be $x$.

According to question,

$\frac{5}{2}(x)-7=23$

$\frac{5x}{2}=23+7$

$\frac{5x}{2}=30$

$x=30\times \frac{2}{5}$

$x=6\times2$

$x=12$

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