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There were some oval and circular shapes in a box.Durai put more circular shapes in the box.Then of the shapes in the box were oval shapes. Later Durai put another oval shapes in the box. of the shapes in the box were oval shapes now.How many curcular shapes were in the box at first?
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Q. There were some oval and circular shapes in a box.Durai put more circular shapes in the box.Then of the shapes in the box were oval shapes. Later Durai put another oval shapes in the box. of the shapes in the box were oval shapes now.How many curcular shapes were in the box at first?
- Define Initial Circular Shapes: Let's call the number of circular shapes at first . After adding circular shapes, the total number of circular shapes becomes .
- Calculate Total Circular Shapes: If of the shapes are oval after adding the circular shapes, then of the shapes are circular.So, of the total shapes equals .
- Calculate Total Shapes: Let's call the total number of shapes in the box after adding the circular shapes . So, .
- Calculate Circular Shapes After Adding Oval Shapes: After adding another oval shapes, of the shapes are oval, which means are circular.So now, of the new total equals the number of circular shapes, which is still .
- Solve for Total Shapes: .
- Substitute and Simplify Equations: Now we have two equations: () ()
- Solve for Total Shapes: We can solve equation () for : .
- Solve for Circular Shapes: Substitute from equation into equation :
- Final Calculation for Circular Shapes: Simplify the equation:
- Final Calculation for Circular Shapes: Now, solve for :.
- Final Calculation for Circular Shapes: Now, solve for : . Subtract from both sides:.
- Final Calculation for Circular Shapes: Now, solve for : . Subtract from both sides:. Subtract from both sides:.
- Final Calculation for Circular Shapes: Now, solve for :
. Subtract from both sides:
. Subtract from both sides:
. Multiply both sides by to solve for :
.
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