# Simple Equations

## Exercise 4.4

**Question 1:** Set up equations and solve them to find the unknown numbers in the following cases:

(a) Add 4 to eight times the number, you get 60.

**Answer:** If number is x then,

*8x + 4 = 60*

Or, *8x = 60 – 4 = 56*

Or, *x = 56 ÷ 8 = 7*

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

**Answer:** If the number is x then,

`x/5 – 4 = 3`

Or, `x/5 = 3 + 4 = 7`

Or, `x = 7 xx 5 = 35`

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

**Answer:** `(3x)/(4) + 3 = 21`

Or, `(3x)/(4) = 21 – 3 = 18`

Or, `3x = 18 xx 4 = 72`

Or, `x = 72 ÷ 3 = 24`

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

**Answer:** `2x – 11 = 15`

Or, `2x = 15 + 11 = 26`

Or, `x = 26 ÷ 2 = 13`

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

**Answer:** `50 – 3x = 8`

Or, `3x = 50 – 8 = 42`

Or, `x = 42 ÷ 3 = 14`

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

**Answer:** `(x + 19)/(5) = 8`

Or, `x + 19 = 8 xx 5 = 40`

Or, `x = 40 – 19 = 21`

(h) Anwar thinks of a number. If he takes away 7 from 5/2 of the number, the result is 23.

**Answer:** `(5x)/(2) – 7 = 23`

Or, `(5x)/(2) = 23 + 7 = 30`

Or, `5x = 30 xx 2 = 60`

Or, `x = 60 ÷ 6 = 12`

**Question 2:** Solve the following:

(a) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. What is the lowest score?

**Answer:** If lowest marks `= x`

Then, `2x + 7 = 87`

Or, `2x = 87 – 7 = 80`

Or, `x = 80 ÷ 2 = 40`

(b) In an isosceles triangle, the base angles are equal. The vertex angle is 40°. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180°).

**Answer:** Let us assume that a base angle `= x`

Then, `2x + 40 = 180`

Or, `2x = 180 – 40 = 140`

Or, `x = 140 ÷ 2 = 70°`

(c) Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each one score?

**Answer:** If Rahul’s score `= x` then Sachin’s score `= 2x`

Then, `x + 2x = 200 – 2 = 198`

Or, `3x = 198`

Or, `x = 198 ÷ 3 = 66`

Rahul’s score = 66

Sachin’s score = 132

**Question 3:** Solve the following:

(a) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. How many marbles does Parmit have?

**Answer:** Let us assume that number of marbles with Parmit `= x`

Then, `5x + 7 = 37`

Or, `5x = 37 – 7 = 30`

Or, `x = 30 ÷ 5 = 6`

(b) Laxmi's father is 49 years old. He is 4 years older than three times Laxmi’s age. What is Laxmi’s age?

**Answer:** Let us assume Laxmi’s age `=x`

Then, `3x + 4 = 49`

Or, `3x = 49 – 4 = 45`

Or, `x = 45 ÷ 3 = 15`

(c) People of Sundargram planted trees in the village garden. Some of the trees were fruit trees. The number of non-fruit trees were two more than three times the number of fruit trees. What was the number of fruit trees planted if the number of non-fruit trees planted was 77?

**Answer:** Let us assume that number of fruit trees `= x`

Then, `3x + 2 = 77`

Or, `3x = 77 – 2 = 75`

Or, `x = 75 ÷ 3 = 25`

**Question 4:** Solve the following riddle:

I am a number,

Tell my identity!

Take me seven times over,

And add a fifty!

To reach a triple century,

You still need forty!

**Answer:** Let us assume the number `= x`

Then, `7x + 50 = 300 – 40 = 260`

Or, `7x = 260 – 50 = 210`

Or, `x = 210 ÷ 7 = 30`