Page 11 - Start Up Mathematics_7

Solution: The amount deposited will be represented by a positive integer.
Amount deposited = + ` 5,000

Amount withdrawn = – ` 3,500
Balance in Mansi’s account = ` 5,000 – ` 3,500 = ` 1,500
Example 5: Vivek and James had a boxing match which extended to five bouts. In the first bout
Vivek gained 5 points. In subsequent bouts, he lost 7 points, gained 4 points, lost 6
points and finally gained 3 points over his opponent James. Who won the match?
Solution: Vivek’s total points in the 5 bouts = +5 – 7 + 4 – 6 + 3
= (5 + 4 + 3) – (7 + 6)
= 12 – 13 = –1
Since, Vivek ended with one negative point, therefore
James won the match. Try It Out!
Example 6: Verify a – (–b) = a + b when a = 30 and b = 12. Fill in the missing numbers
Solution: We have, a – (–b) = 30 – (–12) = 30 + 12 = 42 to complete the magic
square.
Also, a + b = 30 + 12 = 42; hence, a – (–b) = a + b 1 0
–4 –3
Example 7: Use the sign of >, < or = in the box to make the –7
statements true. Hint: In a magic square,
(a) (–7) + (–5) (–7) – (–5) each row, column and

(b) –2 + 13 – (–7) 15 – (–6) + (–3) diagonal has the same sum.

Solution: (a)  (–7) + (–5) = –(7 + 5) = –12 and (–7) – (–5) = –7 + 5 = –(7 – 5) = –2
∴ (–7) + (–5) < (–7) – (–5)
(b)  –2 + 13 – (–7) = (13 + 7) – 2 = 20 – 2 = 18 and
15 – (–6) + (–3) = (15 + 6) – 3 = 21 – 3 = 18
∴ –2 + 13 – (–7) = 15 – (–6) + (–3)

Example 8: A water tank has steps inside it. A monkey is sitting on the topmost step (i.e., the
first step). The water level is at the ninth step.
(a) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps
will he reach the water level?
(b) After drinking water, he wants to go back. For this, he jumps 4 steps up and
then jumps back 2 steps down in every move. In how many jumps will he reach
back the top step?

(c) If the number of steps moved down is represented by negative integers and the
number of steps moved up by positive integers, represent his moves in part (a)
and (b) by completing the following:
(i) –3 + 2 – ____ = –8 (ii) 4 – 2 + ____ = 8
If in (i) the sum (–8) represents going down by eight steps, what will the sum
8 in (ii) represent? (NCERT)
Solution: (a) Let the number of steps moved down be represented by negative integers and
the number of steps moved up by positive integers. Therefore, the movement of
monkey can be represented as –3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3 = –8,
i.e., he has to jump 11 times to reach the water level.

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