Question

a)When a 500 rupee note was changed we got 20 rupee notes 50 rupee notes. Taking number of notes as x and y write an equation showing the total sum?

b)If the total number of notes is 13 form another equation ?

c) Find the number of notes in each category ?

Answer 1

$\large\underline{\sf{Given- }}$

When a 500 rupee note was changed we got 20 rupee notes 50 rupee notes.

☆ Number of 20 rupee note is x

☆ Number of 50 rupee note is y.

So,

☆ Total amount of 20 rupee note = 20x

☆ Total amount of 50 rupee note = 50y

So, total amount of rupee 20 and rupee 50 note is 500.

$\red{\rm :\longmapsto\:20x + 50y = 500}$

☆ In simplified form, its rewritten as

$\rm :\longmapsto\:10(2x + 5y) = 500$

$\rm :\longmapsto\:2x + 5y = 50 - - - (1)$

Now, further given that

☆ Total number of notes is 13.

As it is given that,

☆ Number of 20 rupee note is x

☆ Number of 50 rupee note is y.

So,

$\red{\rm :\longmapsto\:x + y = 13 - - (2)}$

Now, we have 2 linear equations,

$\rm :\longmapsto\:2x + 5y = 50 - - - (1)$

and

$\rm :\longmapsto\:x + y = 13 - - - (2)$

can be rewritten as on multiply by 2,

$\rm :\longmapsto\:2x + 2y = 26 - - - (3)$

Now, Subtracting equation (3) from equation (2), we get

$\rm :\longmapsto\:3y = 24$

$\purple{\rm :\longmapsto\:y = 8}$

On substituting y = 8 in equation (2), we get

$\rm :\longmapsto\:x + 8 = 13$

$\rm :\longmapsto\:x = 13 - 8$

$\pink{\rm :\longmapsto\:x = 5}$

Hence,

• Number of 20 rupee note is 5

• Number of 50 rupee note is 8

Answer 2

Answer:

$\large\underline{\sf{Given- }}$

When a 500 rupee note was changed we got 20 rupee notes 50 rupee notes.

☆ Number of 20 rupee note is x

☆ Number of 50 rupee note is y.

So,

☆ Total amount of 20 rupee note = 20x

☆ Total amount of 50 rupee note = 50y

So, total amount of rupee 20 and rupee 50 note is 500.

$\red{\rm :\longmapsto\:20x + 50y = 500}$

☆ In simplified form, its rewritten as

$\rm :\longmapsto\:10(2x + 5y) = 500$

$\rm :\longmapsto\:2x + 5y = 50 - - - (1)$

Now, further given that

☆ Total number of notes is 13.

As it is given that,

☆ Number of 20 rupee note is x

☆ Number of 50 rupee note is y.

So,

$\red{\rm :\longmapsto\:x + y = 13 - - (2)}$

Now, we have 2 linear equations,

$\rm :\longmapsto\:2x + 5y = 50 - - - (1)$

and

$\rm :\longmapsto\:x + y = 13 - - - (2)$

can be rewritten as on multiply by 2,

$\rm :\longmapsto\:2x + 2y = 26 - - - (3)$

Now, Subtracting equation (3) from equation (2), we get

$\rm :\longmapsto\:3y = 24$

$\purple{\rm :\longmapsto\:y = 8}$

On substituting y = 8 in equation (2), we get

$\rm :\longmapsto\:x + 8 = 13$

$\rm :\longmapsto\:x = 13 - 8$

$\pink{\rm :\longmapsto\:x = 5}$

Hence,

Number of 20 rupee note is 5

Number of 50 rupee note is 8