**ML Aggarwal CBSE Solutions Class 6 Math 12th Chapter Algebra Exercise 12.1**

**Ex 12.1**

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

**Solution:**

(i) In fig. using 2 matchstick One T is formed.

(ii) In fig. using two 2 matchstick one V is formed.

(iii) In fig. using 3 matchstick one Z is formed.

(iv) In fig. using 3 matchstick one U is formed.

(v) In fig. using 4 matchstick one F is formed.

(vi) In fig. using 5 matchstick one S is formed.

**(2) If there are 24 mangoes in a box, how will you write the number of mangoes in terms of the number of boxes? use b for the number of boxes) **

**Solution:** The number of mangoes will depend upon number of boxes.

In the statement, b for the number of boxes, then the total number of mangoes of b boxes is given by the rule:

The total number of mangoes = 24b

**(3) Anuradha is drawing a dot Rangoli (a beautiful patterns of lines joining dots). She has 8 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there is there are 12 rows?**

**Solution: Case 1:** Dots depend upon number of rows .

If the letter r stands for number of rows , then the total number of dots of r rows is given by the rule:

The total number of rows = 8r

**Case 2: **There are 8 dots in a row.

So, Number of dots in 12 rows = 8 x 12 = 96.

**(4) Anu and Meenu are sisters. Anu is 5 years younger than Meenu. Can you write Anu’s age in terms of Meenu’s age? Take Meenu age as x years.**

**Solution: **Anu’s age depends upon Meenu’s age. If Meenu’s age is x years, then Anu’s age = x – 5

**(5) Oranges are to be transferred from larger boxes to smaller boxes. When a larger box is emptied, the oranges from it fill 3 smaller boxes and still 7 oranges are left. If the number of oranges in a small box are taken to x, then what is the number of oranges in the larger box.**

**Solution: **The smaller boxes orange’s depend upon larger box’s oranges.

Oranges are transferred from larger box to smaller box.

Number of oranges in a smaller box are x,

There are in total 3 smaller box are filled up, so total number of oranges in smaller box = 3x

7 oranges are left in larger box.

Then the number of oranges in the larger box = 3x + 7

**(6) Harsha’s score in Mathematics is 15 more than three fourth of her score in Science. If she scores x marks in Science, find her score in Mathematics?**

**Solution: **Harsha’s Mathematics marks depend upon her marks in Mathematics.

Here she scores in Science = x marks

**Three-fourth of her score in science = ¾ x X = 3X/4**

Then her score is said 15 more than three fourth of her score in Science, That’s mean answer is 3X/4 + 4

**(7) Solution: **If the number of triangles formed is x, then the number of matchstick required = 2x + 1

**(8) Solution: **If the number of letter A’s formed is x then the number of matchsticks required = 4x + 2