Translate each of the following statements into an equation, using x as the variable:
(a) 13 subtracted from twice a number gives 3.
(b) One fifth of a number is 5 less than that number.
(c) Two-third of number is 12.
(d) 9 added to twice a number gives 13.
(e) 1 subtracted from one-third of a number gives 1.
(a) 2x − 13 = 3
(b) x/5 = x − 5
(c) 2x/3 = 12
(d) 2x + 9 = 13
(e) x/3 − 1 = 1
Translate each of the following statements into an equation:
(a) The perimeter (p) of an equilateral triangle is three times of its side (a).
(b) The diameter (d) of a circle is twice its radius (r).
(c) The selling price (s) of an item is equal to the sum of the cost price (c) of an item and the profit (p) earned.
(d) Amount (a) is equal to the sum of principal (p) and interest (i).
(a) p = 3a
(b) d = 2r
(c) s = c + p
(d) a = p + i
Let Kanika’s present age be x years. Complete the following table, showing ages of her relatives:
| Situation (described in ordinary language) | Expressions |
|---|---|
| (i) Her brother is 2 years younger. | __________ |
| (ii) Her father’s age exceeds her age by 35 years. | __________ |
| (iii) Mother’s age is 3 years less than that of her father. | __________ |
| (iv) Her grandfather’s age is 8 times of her age. | __________ |
(i) x − 2
(ii) x + 35
(iii) x + 32
(iv) 8x
If m is a whole number less than 5, complete the table and by inspection of the table, find the solution of the equation 2m − 5 = −1 :
| m | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| 2m−5 | −5 | −3 | −1 | 1 | 3 |
Solution is m = 2
A class with p students has planned a picnic. Rs 50 per student is collected, out of which Rs 1800 is paid in advance for transport. How much money is left with them to spend on other items?
50p − 1800
In a village, there are 8 water tanks to collect rain water. On a particular day, x litres of rain water is collected per tank. If 100 litres of water was already there in one of the tanks, what is the total amount of water in the tanks on that day?
8x + 100 L
What is the area of a square whose side is m cm?
m × m sq cm
Perimeter of a triangle is found by using the formula P = a + b + c, where a, b and c are the sides of the triangle. Write the rule that is expressed by this formula in words.
The perimeter of a triangle is the sum of all its sides.
Perimeter of a rectangle is found by using the formula P = 2 ( l + w), where l and w are respectively the length and breadth of the rectangle. Write the rule that is expressed by this formula in words.
The perimeter of a rectangle is twice the sum of its length and breadth.
On my last birthday, I weighed 40kg. If I put on m kg of weight after a year, what is my present weight?
(m + 40) kg
Length and breadth of a bulletin board are r cm and t cm, respectively.
(i) What will be the length (in cm) of the aluminium strip required to frame the board, if 10cm extra strip is required to fix it properly.
(ii) If x nails are used to repair one board, how many nails will be required to repair 15 such boards?
(iii) If 500sqcm extra cloth per board is required to cover the edges, what will be the total area of the cloth required to cover 8 such boards?
(iv) What will be the expenditure for making 23 boards, if the carpenter charges Rs x per board.
(i) 2(r + t) + 10
(ii) 15x
(iii) (8rt + 4000) sq cm
(iv) Rs 23x
Sunita is half the age of her mother Geeta. Find their ages
(i) after 4 years?
(ii) before 3 years?
(i) Sunita: x+4, Geeta: 2x+4
(ii) Sunita: x−3, Geeta: 2x−3
Match the items of Column I with that of Column II:
| Column I | Column II |
|---|---|
| (i) The number of corners of a quadrilateral | (A) = |
| (ii) The variable in the equation 2p + 3 = 5 | (B) constant |
| (iii) The solution of the equation x + 2 = 3 | (C) +1 |
| (iv) solution of the equation 2p + 3 = 5 | (D) −1 |
| (v) A sign used in an equation | (E) p |
| (F) x |
(i) − (B), (ii) − (E), (iii) − (C), (iv) − (D), (v) − (A)