**Algebra**

**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.**

**(a)**A pattern of letter T as

**(b)** A pattern of letter Z as**(c)** A pattern of letter U as

**A pattern of letter V as**

(d)

(d)

**(e)**A pattern of letter E as

**A pattern of letter S as**

(f)

(f)

**A pattern of letter A as**

(g)

(g)

**Solution:**

**(a) For T:**

Clearly, to make one T, we use 2 matchsticks as shown in the figure. Rule is given as

“Number of matchsticks required = 2n”, where n can take any value 1, 2, 3, …

**(b) For Z :**

Clearly, to make one Z, we use 3 matchsticks as shown in the figure. Rule is given as

“Number of matchsticks required = 3 n”, where n can take any value 1, 2, 3, …

**(c) For U :**

Clearly, to make one U, we use 3 matchsticks as shown in the figure. Rule is given as

“Number of matchsticks required = 3n”, where rt can take any value 1, 2, 3, …

**(d) For V :**

Clearly, to make one V, we use 2 matchsticks as shown in the figure. Rule is given as

“Number of matchsticks required = 2n”, where n can take any value 1, 2,3,…

**(e) For E :**

Clearly, to make one E, we use 5 matchsticks as shown in the figure. Rule is given as

“Number of matchsticks required = 5n”, where n can take any value 1, 2, 3, …

**(f) For S :**

Clearly, to make one S, we use 5 matchsticks as shown in the figure. Rule is given as

“Number of matchsticks required = 5n”, where n can take any value 1, 2, 3, …

**(g) For A :**

Clearly, to make one A, we use 6 matchsticks as shown in the figure. Rule is given as

“Number of matchsticks required = 6 n”, where n can take any value 1, 2, 3, …

**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:**

(a) and (d) parts of Q. 1. give the same rule as for L. It happens as the same number of matchsticks are being used in these cases.

**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:**

Since, there are 5 cadets in a row and number of rows are n

∴ Rule is given as

Number of cadets in the parade = 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:**

Since, there are 50 mangoes in a box and b is the number of boxes.

∴ 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:**

Since, there are s number of students and each student having 5 pencils.

∴ Total number of pencils needed = 5n

**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:**

Since, a bird flies at 1 kilometre in one minute. If it flies for t minutes. Total distance covered by 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 10 rows?**

**Solution:**Since, a row contains 9 dots.

Therefore, number of dots in r rows = 9 r.

Number of dots in 8 rows = 9 x 8 = 72

and, number of dots in 10 rows = 9 x 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:**

Let Radha’a age be x years. Since Radha’s younger sister Leela is 4 years younger than Radha.

∴ Leela’s age = (x – 4) year

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

**Solution:**

Number of laddus given to guests and family members = l

Number of laddus left over = 5

Number of laddus made by mother = 1 + 5

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

**Solution:**

Number of oranges in the larger box

= 2 x Number of oranges iR small box + oranges left over

= 2x +10

where x is. the number of oranges in the small box.

**Question 11.****(a)** Look at the following matchstick pattern of squares (see figure). The squares are not separate. Two neighbouring squares have a common matchstick. Observe the pattern and find the rule that gives the number of matchsticks in terms of the number of squares.**(b)** Figure gives a matchstick pattern of triangles. As in Exercise 11(a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.

**Solution:**

(a) Clearly, from the figure:

(a) Clearly, from the figure:

Thus, rule is as under:

Number of matchsticks = 3x +1, where x is the number of squares,

**(b) Clearly, from the figure :**

Thus, rule is as under: ,

Number of matchsticks = 2x +1, where x is the number of triangles.