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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].
To do:
We have to set up an equation in the given cases.
Solution:
(i) Let Parmit have $m$ number of marbles
Then, Irfan has $(5m+7)$ marbles
Total number of marbles Irfan has $=37$
So, $5m+7=37$
(ii) Let the age of Laxmi be $y$ years
Laxmi’s father is four years older than three times Laxmi’s age.
Then Laxmi's father's age $=3y+4$ years
Also, the age of Laxmi’s father is 49 years.
According to the question, $3y+4=49$
(iii) Let the lowest marks obtained by the student be $l$
Then the highest marks obtained by the student is $2l+7$
And the highest score is $87$
Therefore, according to the question, $2l+7=87$
(iv) Let the base angle of a triangle be $b$.
Then the vertex angle of the isosceles triangle$=2b$.
According to the question, $b+b+2b=180^{\circ}$ [Since the sum of angles of a triangle is 180 degrees]
Thus, $4b=180^{\circ}$