Question

(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find .
them.
Gin The coach of a cricket team buys 7 bats and 6 balls for 3800. Later, she buys 3.​

Answer 1

Step-by-step explanation:

2x-18=180

2x=18+180

2x=198

x=198/2

x=99

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Answer 2

Solution 1:

$\bf{\small{\red{\underline{\bf{Given\::}}}}}$

The larger of two supplementary angles exceeds the smaller by 18°.

$\bf{\small{\red{\underline{\bf{To\:find\::}}}}}$

The angles.

$\bf{\small{\red{\underline{\bf{Explanation\::}}}}}$

Let the two angles be r° and m°.

We know that supplementary angle be 180°

A/q

$\mapsto\sf{r\degree + m\degree=180\degree.................(1)}$

&

$\mapsto\sf{r\degree=m\degree+18\degree..................(2)}$

So;

Putting the value of r in equation (1),we get;

$\longrightarrow\sf{m\degree+18\degree+m\degree=180\degree}\\\\\longrightarrow\sf{2m\degree+18\degree=180\degree}\\\\\longrightarrow\sf{2m\degree=180\degree-18\degree}\\\\\longrightarrow\sf{2m\degree=162\degree}\\\\\longrightarrow\sf{m=\cancel{\dfrac{162}{2} }}\\\\\longrightarrow\sf{\red{m=81\degree}}$

Putting the value of m in equation (2),we get;

$\longrightarrow\sf{r=81\degree+18\degree}\\\\\longrightarrow\sf{\red{r=99\degree}}$

Thus;

The angles are r = 99° and m = 81° .

Solution 2:

$\bf{\small{\red{\underline{\bf{Correct\:Question\::}}}}}$

The coach of a cricket team buys 7 bats and 6 balls for 3800.Later, she buys 3 bats and 5 balls for Rs.1750.Find the cost of each bats and each balls.

$\bf{\small{\red{\underline{\bf{Explanation\::}}}}}$

Let the cost of one bat be Rs.r

Let the cost of one ball be Rs.m

So, the equation formed, we get;

$\mapsto\sf{7r+6m=3800.........................(1)}\\\\\mapsto\sf{3r+5m=1750..........................(2)}$

$\green{\underline{\underline{\bf{Using\:Substitution\:Method\::}}}}}$

From equation (1),we get;

$\mapsto\sf{7r+6m=3800}\\\\\mapsto\sf{7r=3800-6m}\\\\\mapsto\sf{r=\dfrac{3800-6m}{7} .........................(3)}$

Putting the value of r in equation (2),we get;

$\longrightarrow\sf{3\bigg(\dfrac{3800-6m}{7} \bigg)+5m=1750}\\\\\\\longrightarrow\sf{\dfrac{11400-18m}{7} +5m=1750}\\\\\\\longrightarrow\sf{11400-18m+35m=12250}\\\\\\\longrightarrow\sf{11400+17m=12250}\\\\\\\longrightarrow\sf{17m=12250-11400}\\\\\\\longrightarrow\sf{17m=850}\\\\\\\longrightarrow\sf{m=\cancel{\dfrac{850}{17} }}\\\\\\\longrightarrow\sf{\red{m=Rs.50}}$

Putting the value of m in equation (3),we get;

$\longrightarrow\sf{r=\dfrac{3800-6(50)}{7} }\\\\\\\longrightarrow\sf{r=\dfrac{3800-300}{7} }\\\\\\\longrightarrow\sf{r=\cancel{\dfrac{3500}{7} }}\\\\\\\longrightarrow\sf{\red{r=Rs.500}}$

Thus;

The cost of one bat be Rs.500.

The cost of one ball be Rs.50.