Page 214 - Start Up Mathematics_6

Solution: Let Sita’s age be x years.

Since Sita is 7 years younger, therefore Radha is 7 years older.
Hence, Radha’s age = (x + 7) years
Example 6: Some apples are to be transferred from a large box into smaller boxes. When the
large box is emptied, the apples from it fill three smaller boxes and still 5 apples
remain outside. If the number of apples in a small box are taken to be x, what was
the number of apples in the large box?
Solution: Let the number of apples in a small box be x.
Apples in the large box = (number of apples in three smaller boxes) + 5 = 3x + 5

Example 7: The following patterns are formed using matchsticks. Find the general rule that
gives the number of triangles formed and the number of matchsticks used in the nth
pattern.

, , , ... .

Pattern 1 Pattern 2 Pattern 3

Solution: On observing the given pattern, we obtain the rules tabulated below:
Pattern 1 2 3 4 ... n
Number of triangles 2 4 6 8 ... 2n
Number of matchsticks 5 9 13 17 ... 4n + 1

EXERCISE 11.1

1. Observe the following pattern, identify the variable and write the general expression that
gives the cost of chocolates in terms of the number of chocolates.

Number of chocolates 1 2 3 4 ... n
Cost of chocolates bought for ` 5 each 5 10 15 20 ... ...

2. Observe the following pattern, identify the variable and write the general expression of
number of legs in terms of the number of houses.

Number of horses in a stable 1 2 3 4 ... n
Total number of legs in stable 4 8 12 16 ... ...

3. Observe the following pattern, identify the variable and write the general rule that gives
the number of legs in terms of the number of chicks:

Number of chicks 1 2 3 4 ... n
Total number of legs 2 4 6 8 ... ...

4. Observe the following pattern, identify the variable and write the general expression:
1, 4, 9, 16, 25, ... .

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