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Maria mixes white paint and red paint in the ratio 2 : 3 - OCR - GCSE Maths - Question 18 - 2017 - Paper 1
Question 18
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 18 - 2017 - Paper 1
Step 1
Calculate the amount of white and red paint initially
Answer
The total ratio of white to red paint is 2:3, which gives a total of 5 parts (2 + 3). To find the amount of each color:
- White paint = ( \frac{2}{5} \times 15 ) litres = 6 litres
- Red paint = ( \frac{3}{5} \times 15 ) litres = 9 litres
Step 2
Determine the new amount needed for the 1 : 5 ratio
Answer
Let the amount of additional red paint to be added be ( x ) litres. The new amount of red paint will be ( 9 + x ) litres. For the ratio of white to red paint to be 1:5, we have the equation: [ \frac{6}{9+x} = \frac{1}{5} ] Cross-multiplying gives: [ 6 \times 5 = 1 \times (9 + x) ] [ 30 = 9 + x ] [ x = 30 - 9 ] [ x = 21 ]