question_answer 6)

Set up an equation in the following cases: (i) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. (Take m to be the number of Parmit's marbles.) (ii) Laxmi's father is 49 years old. He is 4 years older than three times Laxmi's age. (Take Laxmi's age to be y years.) (iii) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest Score is 87. (Take the lowest score to be l.) (iv) In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle   be b in degrees. Remember that the sum of angles of a triangle is 180 degrees).

Answer:

                (i) Let Parmit has m marbles. Then, five times the marbles Parmit has \[=\text{5m}\] Irfan has 7 marbles more than five times the marbles Parmit has \[=\text{5m }+\text{ 7}\], i.e., Irfan has (5m + 7) marbles But it is given that Irfan has 37 marbles. Therefore,          \[5m+7=37\] (ii) Let the age of Laxmi be y years. Then, three times Laxmi's age = 3y years                                                   Laxmi's father is 4 years older than three times Laxmi's age, i.e., Age of Laxmi's father        \[=(3y+4)\] years But it is given that Laxmi's father is 49 years old Therefore,        \[\text{3y}+\text{4}=\text{49}\] (iii) Let the lowest marks be \[l\], Then, twice the lowest marks \[=2l\] Highest score obtained by a student in her class is twice the lowest marks plus 7, i.e., Highest score     \[=2l+7\] But this is given to be 87 Therefore,  \[2l+7=87\] (iv) Let the base angle be b in degrees. Let the vertex angle be a in degrees. \[\because \] Sum of the angles of a triangle is 180 degrees. \[\therefore \] \[a+b+b={{180}^{o}}\]or \[a+2b={{180}^{o}}\]