Question

A sum of $2700 is to be given in the form of 63 prizes. If the prize is of either $100 or $25, find the number of prizes of each type. Please explain the steps!!!

Answer 1

Answer:

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Answer 2

$\Large{\underline{\underline{\bf{Solution :}}}}$

As, it is given that total money = $2700

So,

A.T.Q

Let the prizes given in form of $100 be a

Let the prizes given in form of $25 be b.

So,

A.T.Q

→ a + b = 63 .....(1)

$\sf{→ 100a + 25b = 2700}$

$\sf{→ 25(4a + b) = 2700}$

$\sf{→ 4a + b = \frac{\cancel{2700}}{\cancel{25}}}$

$\sf{→ 4a + b = 108}$

$\rule{150}{2}$

★ Subtracting equation (1) and (2).

We get,

$\sf{→ 3x = 45} \\ \\ \sf{→ x = \frac{\cancel{45}}{\cancel{3}}} \\ \\ \sf{→a = 15}$

$\therefore$ Prizes given in form of $100 is 15 prizes.

$\rule{150}{2}$

Now, Put Value of a in equation (1).

$\sf{→ 15 + y = 63} \\ \\ \sf{→ y = 63 - 15} \\ \\ \sf{→ y = 48}$

$\therefore$ Prizes given in the form of $25 is 48 prizes.