Jane collected 53 dollar notes for the competition of which x are $2 notes and y is $10 notes. The total value of the dollar notes is $394. Form 2 equations in terms of x and y. Solve the equations and hence find the number of $2 notes

Answer 1

What you know:
1. Jane collected 53 dollar notes
2. Jane collected a total of $394
3. There are $2 notes (x number were collected)
4. There are $10 notes (y number were collected)

First Equation:
Since you know that Jane collects a total amount of 53 dollar notes you can begin an equation. 53 = something.

You also know that there are only two types of notes being collected ($2 and $10) and you know that x and y represent how many Jane collects.

Therefore: 53 = x + y
(which can also be written as x + y = 53)

Second Equation:
Since you know the total value of the notes that Jane collects to be $394 you can begin to set up an equation.
394 = something.

You also know that there are only two kinds of notes ($2 and $10) and that the number of notes collected are represented by x and y.
In order to find the cost of something if you are given price and quantity you would need to multiply. (example. you have five $10 bills. that would mean that you have $50. because 10*5 = 50)

So. $2 and x go together
and $10 and y go together

Therefore 394 = 2x + 10y

(I hope this helped. I realize it became rather long. I'll work on length for future posts.)