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Q1. Evaluate the expression: (a) vw - v = ? ( for v = 6 and w = 3 ) (b) 8z + 5 = ? ( for z = 9 )

Solution

Here we have to put the values of the variables given in the bracket. (a) vw - v Put v = 6 and w = 3 i.e. vw - v = (6 x 3) - 6 = 18 - 6 = 12 (b) 8z + 5 Put z = 9 i.e. 8z + 5 = (8 x 9) + 5 = 72 + 5 = 77

Q2. Sumitra has Rs 34 in denominations of 50 paisa and 25 paisa coins. If the number of 25 paisa coins is twice the number of 50 paisa coins, then how many coins of each type does she has in all?

Solution

Let the number of 50 paisa coins = x Then, number of 25 paisa coins = 2x Total money with Sumitra = Rs 34 = 34 × 100 paise = 3400 paiseFrom the given condition, we have: 50x + 25 × 2x = 3400 50x + 50x = 3400 100x = 3400 x = 34 Number of 50 paisa coins = 34 Number of 25 paisa coins = 2 × 34 = 68

Q3. A sum of Rs. 500 is in denominations of Rs. 5 and Rs. 10. If the total number of notes is 90, find the number of notes of each type?

Solution

Let the number of 5 Rupee note = x Then the number of 10 Rupee note = 90 - x Total money = Rs. 500 As per the given condition, 5x + 10(90 - x) = 500 5x + 900 - 10x = 500 -5x = -400 x = 80Hence, number of 5 Rupee note = 80And, number of 10 Rupee note = (90 - 80) = 10

Q4. Find the value of t if 10 = 4 + 3(t + 2).

Solution

Equation is 10 = 4 + 3(t + 2) Transpose 4 to L.H.S. 10 - 4 = 3(t + 2)i.e. 6 = 3t + 6 Divide both the sides by 3, 2 = t + 2 Subtract 2 from both the sides t = 0

Q5. Which equation illustrates this situation? (a) There are 12 golf balls in a bucket. There are x white golf balls and 5 blue golf balls. (b) You have x oranges in your bag. Your sister has 4 times as many oranges as you have. Your sister has 36 oranges.

Solution

Here we have to form equations according to the situation given. (a) Total number of Golf balls = 12 White balls = x Blue balls = 5 It can be written as x + 5 = 12 (b) Number of oranges = x 4 times oranges = 4x It can be written as 4x = 36