## Algebra Exercise – 11.1

**Question 1. Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.**

**Solution:**

1. Number of matchsticks required to make one =2

∴ Number of matchsticks required to make a pattern of letter T as =2n

2. Number of matchsticks required to make one = 3

∴ Number of matchsticks required to make a pattern of letter Z as = 3n

3. Number of matchsticks required to make one = 3

∴ The number of matchsticks required to make a pattern of the letter U is = 3n

4. Number of matchsticks required to make one = 2

∴ Number of matchsticks required to make a pattern of letter V as = 2n

5. Number of matchsticks required to make one = 5

∴ Number of matchsticks required to make a pattern of letter E as = 5n

6. Number of matchsticks required to make one = 5

∴ The number of matchsticks required to make a pattern of the letter S is = 5n

7. Number of matchsticks required to make one = 6

∴ The number of matchsticks required to make a pattern of letter A is = 6n

**Question 2. We already know the rule for the pattern of letters L, C and F. Some of the letters from Q.1 (given above) give us the same rule as that given by L. Which are these? Why does this happen?**

**Solution:**

Part (a) & (d) i.e., letters T and V have the same rule as that given by L. Because the number of matchsticks required in each of them is 2.

**Question 3. Cadets are marching in a parade. There are 5 cadets in a row. What is the rule which gives the number of cadets, given the number of rows? (Use n for the number of rows.)**

**Solution:**

Let the number of rows = n

Number of cadets in each row = 5

Therefore, the total number of cadets = 5n

**Question 4. If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes.)**

**Solution:**

Let the number of boxes = b

Number of mangoes in each box = 50

Therefore, the total number of mangoes = 50b

**Question 5. The teacher distributes 5 pencils per student. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students.)**

**Solution:**

Let the number of students = s

Number of pencils distributed to each Student = 5

Therefore, the total number of pencils needed = 5s

**Question 6. A bird flies 1 kilometre in one minute. Can you express the distance covered by the bird in terms of its flying time in minutes? (Use t for flying time in minutes.)**

**Solution:**

Let the flying time of the bird be two minutes.

Distance covered by the bird in minute =1 km

∴ Distance covered by the bird in t minutes =1 x t km = t km

**Question 7. Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots) with chalk powder. She has 9 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 1 0 rows?**

**Solution:**

The number of dots in each row = 9

Number of rows = r

Therefore, the total number of dots = 9r

When there are 8 rows, then the number of dots = 9 x 8 = 72

When there are 10 rows, then the number of dots = 9×10 = 90

**Question 8. Leela is Radha’s younger sister. Leela is 4 years younger than Radha. Can you write Leela’s age in terms of Radha’s age? Take Radha’s age to be x years.**

**Solution:**

Radha’s age = x years

Since Leela is 4 years younger than Radha.

Therefore, Leela’s age = (x- 4) years.

**Question 9. Mother has made laddus. She gives some laddus to guests and family members; still, 5 laddus remain. If the number of laddus’s mother gave away is l, how many laddus did she make?**

**Solution:**

Number of laddus gave away = l

Number of remaining laddus = 5

∴ Total number of laddus = (l + 5)

**Question 10. Oranges are to be transferred from larger boxes into smaller boxes. When a large box is emptied, the oranges fill two smaller boxes, and 10 oranges remain outside. If the number of oranges in a small box is taken to be x, what is the number of oranges in the larger box?**

**Solution:**

Number of oranges in a small box = x

Number of smaller boxes = 2

Therefore, the total number of oranges in smaller boxes = 2x

Number of remaining oranges = 10

Thus, the number of oranges in the larger box = 2x + 10

**Question 11. 1. Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring squares have a common matchstick.**

**Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint: If you remove the vertical stick at the end, you will get a pattern ofCs.)**

**2. The given figure gives a matchstick pattern of triangles. As in Exercise 11 (a) above, find the general rule that shows the number of matchsticks in terms of the number of triangles.**

**Solution:**

If we remove 1 matchstick from each figure, then they make multiples of 3, i.e., 3, 6, 9, 12, 8,

So the required equation = 3x + 1, where x is number of squares

If we remove 1 matchstick from each figure, then they make multiples of 2, i.e., 2, 4, 6,8…

So the required equation = 2x + 1, where x is several triangles.