Question

Set up equations and solve them to find 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.

Answer 1

Hint: Here, we may just follow the steps which each statement says and write equations according to that, on solving the equations so formed we may get the required unknown numbers.

Complete step-by-step solution -
So at first we are going through the case (a):
Let us consider the required unknown number be =x.
So, eight times of this number will be 8x.
Now on adding 4, it becomes 8x + 4, so according to question we have:
$8x+4=60$
Or, $8x=60-4$
Or, $x=\dfrac{56}{8}$
Or, $x=7$
Hence for question (a) required number is =7.

Now, for the case (b):
Let us consider the required number be = y
So, one fifth of the number will be =$\dfrac{y}{5}$
As it is given that on subtracting 4 from the one-fifth of the number we will get 3, we have the following equation:
$\dfrac{y}{5}-4=3$
Or, $\dfrac{y-20}{5}=3$
Or, $y=15+20$
So, y = 35
Hence, for question (b) unknown number is 35.

Now, for case (c):
Let the required number be = z.
Now according to question when we add 3 to the three-fourth of this number (z) we get 21, so we have the following equation:
$\dfrac{3}{4}z+3=21$
Or, $\dfrac{3}{4}z=21-3$
Or, $z=\dfrac{18\times 4}{3}$
Or, z = 24
Hence, for question (c) the unknown number is 24.

Now, for case(d):
Let the required number be =p
According to question when we subtract 11 from twice the number (p) , we will get 15, so we have following equation:
$2p-11=15$
Or, $2p=15+11$
Or, $p=\dfrac{26}{2}$
So, p = 13
Hence, for question (d) the unknown number is 13.

Now for case (e):
Let the number of notebooks Munna has = q.
Now according to question when Munna subtracts thrice the number of notebooks (q) he has from 50 he gets 8, so equation formed will be:
$50-3q=8$
Or, $3q=50-8$
Or, $q=\dfrac{42}{3}$
So, q =14
Hence, for question (e) the unknown number or the number of books Munna has is 14.

Now for case (f):
Let us consider that the number that Ibenhal think is =r
Now, according to the question if she adds 19 to the number and divides the sum by 5, she will get 8. So, the equation formed will be:
$\dfrac{r+19}{5}=8$
Or, $r+19=5\times 8$
Or, r = 40 – 19
Or, r = 21
Hence, for question (f) the unknown that Ibenhal thinks of is 21.

Note: While forming the equations the statements must be read carefully. There are chances of mistakes if addition or subtraction is done from the other number. Follow BODMAS rules wherever necessary.