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Maria mixes white paint and red paint in the ratio 2 : 3 - OCR - GCSE Maths - Question 6 - 2017 - Paper 1
Question 6
Maria mixes white paint and red paint in the ratio 2 : 3. She makes a total of 15 litres of paint. How much more red paint does she need to add to the mixture so th... show full transcript
Worked Solution & Example Answer:Maria mixes white paint and red paint in the ratio 2 : 3 - OCR - GCSE Maths - Question 6 - 2017 - Paper 1
Step 1
Calculate the current amounts of white and red paint
Answer
Given the ratio of white to red paint is 2:3, for a total of 15 litres:
- Let the amount of white paint be ( 2x ) and red paint be ( 3x ).
- Therefore, ( 2x + 3x = 15 ) which gives ( 5x = 15 )
- Solving for ( x ), we find ( x = 3 ).
- Thus, white paint amount is ( 2 \times 3 = 6 ) litres and red paint amount is ( 3 \times 3 = 9 ) litres.
Step 2
Determine how much red paint is needed
Answer
We need to find how much more red paint ( y ) is required so that the new ratio of white to red becomes 1:5:
- The new amount of red paint will be ( 9 + y ) litres.
- Set up the equation for the new ratio: [ \frac{6}{9 + y} = \frac{1}{5} ]
- Cross-multiplying gives: [ 6 \times 5 = 1 \times (9 + y) ]
- This simplifies to: [ 30 = 9 + y ]
- Therefore: [ y = 30 - 9 = 21 ] litres.
Thus, Maria needs to add 21 litres of red paint.