Simple equations STD VI

The organizers of an essay competition decide that a winner in the competition gets a prize of $ 100 and a participant who does not win gets a prize of $ 25. The total prize money distributed is $ 3,000. Find the number of winners, if the total number of participants is 63.

Answer:

Let the number of winners be y

So, number of students who did not win = 63 – y

Given that, 100y + (63 – y )25 = 3000

Or, 100y + 1575 – 25y = 3000

Or, 75y = 3000 – 1575

Or, y = 1425/75

Or, y = 19.

I have a total of $ 300  in notes of denomination $ 1, $ 2 and $ 5. The number of $ 2  notes is 3 times the number of $ 5 notes. The total number of notes is 160. How many notes  of each denomination are with me?

Answer:

Let the number of $5 denomination note be y

So, number of $2 denomination note is 3y

So, number of $1 denomination note = 160 – y – 3y = 160 -4y

Given, 5y + 2x3y +1x (160 – 4y) = 300

Or, 5y +6y + 160 – 4y = 300

Or, 7y = 140

Or, y = 20

The number of $5 denomination note is 20

So, number of $2 denomination note is 3y = 60

So, number of $1 denomination note = 160 - 4y = 80