A girl bought some pencils, erasers, and paper clips at the stationery store. The pencils cost IDR. 1000 each, the erasers cost
IDR. 500 each and the paper clips cost 2 for IDR. 100. If she bought total cost IDR. 10000, how many of each did she buy ?
I wrote :
Pencil = X = IDR. 1000
Eraser = Y = IDR. 500
Paper Clip = IDR. 100/2 = IDR.50
1000X + 500Y + 50Z = 10000
Then ? I'm confuse...
How to solve ?
divide your equation by 50
20x + 10y + z = 200
remember that x, y, and z must be positive whole numbers.
Are we allowed to have zero of any of them ????
I will let you decide that
z = 200 - 20x - 10y
maximum value of x has to be 9, (if x=10, z = 0)
maximum value of y has to be 19
So there are multiple answers.
You could set up a chart to show them
x y z
1 1 170
1 2 160
1 3 150
...
1 17 10
1 18 0 ---> but it said she bought "some", so I guess we should allow that
1 19 -10 ----- NO
2 1 150
...
9 1 10
9 2 0 --- ???
9 3 -10 ---NO
To solve this problem, you can use a system of equations. Let's assign variables to represent the quantities of each item bought.
Let's say:
Pencil = X
Eraser = Y
Paper Clip = Z
Since the pencil costs IDR 1000 each, the total cost of the pencils is 1000X.
Similarly, the erasers cost IDR 500 each, so the total cost of the erasers is 500Y.
As for the paper clips, they cost IDR 50 each, and since she bought 2 for IDR 100, the total cost of the paper clips is 50Z.
Now, we can set up the equation based on the information given:
1000X + 500Y + 50Z = 10000
To solve this equation, we need to find the values of X, Y, and Z that satisfy this equation.
Since we don't have any other information or restrictions, there are multiple possible solutions for this problem.
One solution is to assign values to X, Y, and Z and check if they satisfy the equation:
Let's assume X = 5, Y = 10, and Z = 10.
Substituting these values into the equation:
1000(5) + 500(10) + 50(10) = 10000
5000 + 5000 + 500 = 10000
10000 = 10000
So, X = 5, Y = 10, and Z = 10 is one possible solution, meaning the girl bought 5 pencils, 10 erasers, and 10 paper clips.
However, keep in mind that there may be other combinations of X, Y, and Z that also satisfy the equation.