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
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.)
To form the equations, we can use the given information:
1. The total number of dollar notes collected is 53.
2. The value of each $2 note is $2, and the value of each $10 note is $10.
3. The total value of the dollar notes collected is $394.
Let's form the equations:
Equation 1: The total number of dollar notes collected is 53.
x + y = 53
Equation 2: The total value of the dollar notes collected is $394.
2x + 10y = 394
Now we have a system of equations with two variables (x and y). We can solve this system to find the values of x and y.
To solve the system of equations, we can use either substitution or elimination method. Let's use the elimination method:
Multiply Equation 1 by 2 to eliminate x:
2(x + y) = 2(53)
2x + 2y = 106
Now subtract Equation 2 from the modified Equation 1:
(2x + 10y) - (2x + 2y) = 394 - 106
8y = 288
Divide both sides of the equation by 8:
y = 288/8
y = 36
Now substitute the value of y into Equation 1 to find x:
x + 36 = 53
x = 53 - 36
x = 17
Therefore, the number of $2 notes collected is 17.