Question

A total amount of ₹80,000 is to be distributed among 200 people as prizes. A prize is either of ₹500 or ₹100. Find the number of each prize.

Answer 1

----------------------------------------

Here is the solution:

----------------------------------------

Define x:

Let the number of ₹500 prize be x

The number of ₹100 prize = (200 - x)

Form equation:

500x + 100(200 - x) = 80000

Solve x:

500x + 100(200 - x) = 80000

500x + 20000 - 100x = 80000

400x + 20000 = 80000

400x = 60000

x = 150

Find the number of each prize:

₹500  = x = 150

₹100 = 200 - x = 200 - 150 = 50

Answer: There are 150 ₹500 prize and 50 ₹100 prize.

Answer 2

${\red{\underline{\underline{\large{\mathtt{Question:-}}}}}}$

A total amount of ₹80,000 is to be distributed among 200 people as prizes. A prize is either of ₹500 or ₹100. Find the number of each prize.

${\red{\underline{\underline{\large{\mathtt{Solution:-}}}}}}$

Let the number of ₹500 prize be x

The number of ₹100 prize = (200-x)

$\underline\green{\star{\:\textsf{Equation:-}}}$

$\bf\red{500x\:+\:100(200-x)=80,000}$

$\implies500x + 20000 - 100x = 80000 \\ \implies (500x - 100x) + 20000 = 80000 \\ \implies400x + 20000 = 80000 \\ \implies400x = 80000 - 20000 \\ \implies400x = 60000 \\ \implies \: x = \cancel \frac{60000}{400} = 150 \\ \\ \mathtt \red{x = 150}$

Number of Each prize

₹500 = x = 150

200-x = 200-150 = 50

There are 150 ₹500 prizes and 50 ₹100 prize.

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

⎯⎯⎯⎯⎯