[Exercise- Page 166]
E.7.1. What is meant by the following algebraic expressions?
Solution:
E.7.2. Express the following relations in algebraic expressions, using the processing symbols:
I. Add four times y to five times x
II. Subtract 3 times a number from double of another number
III. Shawpna bought four oranges at the rate of x taka per dozen, one dozen banana at the rate of y taka per four, from a shop. How much did Shawpna spend?
IV. Multiply a by b, then divide the product obtained by 7 times c.
V. If there are x number of bubble gums in a packet, then how many bubble gums are there in the picture?
VI. Robin bought five chocolates for his sister and three for each of his friends. How many chocolates did he buy in total?
Solution:
E.7.3. The cost of an exercise book is x taka, cost of a pencil is y taka and cost of an eraser is z taka.
a) How much did Mita spend, buying one dozen exercise books and half a dozen pencils?
b) Shajib bought eight pencils and two erasers. How much did he spend?
c) Pryanka bought three exercise books, four pencils and one eraser and gave the shopkeeper a 100 taka note. How much did the shopkeeper return Pryanka?
Solution:
E.7.4. Add the following:
(i) 2a + 3b, -a - 2b
(ii) 4x - 5y, -2x + y, 6x + 7y
(iii) 7x + 5y + 2z, 3x - 6y + 7z, -9x + 4y + z
(iv) 5ax + 3by - 14cz, -11by - 7ax - 9cz, 3ax + 6by - 8cz
(v) 12x + 15y - 10z, 15z - 24x - 9y, -6y + 12x - 5z
Solution:
E.7.5. Subtract the second expression from the first expression:
(i) 12a + 23b, 7a - 2b
(ii) 4x - 5y, 6x + 7y
(iii) 10x + 5y + 20z, -9x + 4y + 25z
(iv) 5px + 8qy - 14rz, 11qy - 7px + 9crz
(v) 20x - 5y + 30z, 15z + 4x - 9y
Solution:
E.7.6.
a) Find the perimeter of the board
b) Find the area of the board.
Solution:
E.7.7. The following picture is a pattern made by marbles. How many marbles will be required to make the 100th column?
Solution:
E.7.8. Suppose you want to make a soup of your choice at home. Make a list of the ingredients you will need for that. If many people want to have that soup, then express the ingredients of the soup and the number of people using an algebraic expression.
Solution:
E.7.9. If x = 5a + 7b + 9c, y = b - 3a - 4c, z = c - 2b + a then show that, x + y + z = 3(a + 2b + 2c)
Solution:
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