ML Aggarwal CBSE Solutions Class 6 Math 12th Chapter Algebra Exercise 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.
(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