Question

Q2 Solve the following. 1. 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.What is the lowest score?

2. in an isosceles triangle the base angles are equal. The vertex angle is 40 degree. what are the base angles of triangle?

3. Sachin's scored twice as many runs as Rawal. Together, their runs well too short of a double century. how many runs did each one score?​

Answer 1

Solution :-

• In first question it is given that the class highest marks obtained by a student is twice the lowest marks plus 7

To find → Lowest marks

• According to first question

✶Let the lowest be x

• Total highest score = 87

→ 2x + 7 = 87

→ 2x = 87 - 7

→ 2x = 80

→ x = 80/2 = 40

•°• Lowest marks is 40

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• In second question the base angle of isosceles triangle are equal and the vertex angle is 40°

To find → Base angles of triangle

• According to second question

As we know that

★ Sum of three angle of a triangle is equal to 180°

✶So, let the base of a triangle be x

→ x + x + 40° = 180

→ 2x + 40° = 180

→ 2x = 180 - 40

→ 2x = 140

→ x = 140/2 = 70°

•°• Base angles of isosceles triangle are 70°

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• In third question Sachin's scored twice as many runs as Rawal. Together, their runs well two short of a double century.

To find → Runs did each one score.

• According to third question

✶Let the Rawal's score be x then Sachin's score be 2x

★ Together, their runs well two short of a double century.

→ x + 2x = 200 - 2

→ 3x = 198

→ x = 198/3

→ x = 66

•°• Rawal's score = x = 66

•°• Sachin's score = 2x = 132

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Answer 2

Answer :-

★ Concept :-

Here the concept of Linear Equations in One Variable has been used. According to this, in equations we use constant and variable terms. Where we find the value of variables using constants.

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★ Solution :-

1.) 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. What is the lowest score ?

Answer.) Let the lowest score of the class be 'x', Then.

Given,

» Highest score of the class = 87

» Highest score is equal to the twice of lowest score added 7.

Then, making this into equation, we get,

✒ 2x + 7 = 87

✒ 2x = 87 - 7

✒ 2x = 80

$\: \: \therefore \: \bold{\sf{x} \: = \: \dfrac{80}{2}}$

Hence, the value of x = 40.

So,

$\: \: \underline{\boxed{\sf{\blue{The \: lowest \: mark \: of \: the \: class \: is \: \underline{40}}}}}$

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2.) In an isosceles triangle the base angles are equal. The vertex angle is 40 degree. What are the base angles of triangle ?

Answer.) Let each of the base angle be 'x', then,

Its given that, vertex angle = 40°.

We know that, by Angle Sum Property of the triangle,

• Sum of the angles of Triangle = 180°

By applying, this with equation, we get,

✒ 40° + x° + x° = 180°

✒ 2x° = 180° - 40°

✒ 2x° = 140°

$\: \: \therefore \: \bold{\sf{x} \: = \: \dfrac{140}{2}}$

Hence, the value of x = 70°

So,

$\: \:\underline{\boxed{\sf{\red{The \: value \: of \: each \: of \: the \: base \: angle \: is \: \underline{70°}}}}}$

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3.) Sachin's scored twice as many runs as Rawal. Together, their runs were two short of a double century. How many runs did each one score?

Answer. ) Let the Rawal's score be 'x'. Then, according to the question, Sachin's score is '2x'.

We know that, Double Century = 200 runs

And two less in double century = 200 - 2 = 198 runs.

So, by applying this with equation, we get,

✒ x + 2x = 200 - 2

✒ 3x = 200 - 2

✒ 3x = 198

$\: \: \therefore \: \bold{\sf{x} \: = \: \dfrac{198}{3}}$

Hence, the value of x = 66 runs

And, the value of 2x = 2(66) = 132 runs.

So,

$\: \: \underline{\boxed{\sf{\purple{The\: score \: of \: Rawal \: is \: \underline{66} \: runs \: the \: score \: of \: Sachin \: is \: \underline{132} \: runs }}}}$

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$\:\:\:{\boxed{\sf{\green{A \: glance \: at \: supplementary \: artefacts \: please \: !! \:}}}}$

• About Polynomials :- Polynomial is a vast term related to coefficients and variables. This term shows how an equation is formed using constant terms and variable terms.

• On the basis of degrees, Polynomials are classified as :-

1. Linear Polynomial
2. Quadratic Polynomial
3. Cubic Polynomial
4. Bi - Quadratic Polynomial

• Linear Equations in Two Variable is a seperate case of polynomials where we use two variable terms simultaneously.