Higher June 2019 Paper 1 Q22
22 There are only \(r\) red counters and \(g\) green counters in a bag.
A counter is taken at random from the bag.
The probability that the counter is green is \(\dfrac{3}{7}\)
The counter is put back in the bag.
2 more red counters and 3 more green counters are put in the bag.
A counter is taken at random from the bag.
The probability that the counter is green is \(\dfrac{6}{13}\)
Find the number of red counters and the number of green counters that were in the bag originally. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 12 red, 9 green | P1 | for process to find a relationship between \(r\) and \(g\) eg \(\dfrac{g}{r + g} = \dfrac{3}{7}\) or \(\dfrac{g}{r} = \dfrac{3}{4}\) |
| P1 | for process to find a second relationship between \(r\) and \(g\) eg \(\dfrac{g + 3}{r + 2 + g + 3} = \dfrac{6}{13}\) or \(\dfrac{g + 3}{r + 2} = \dfrac{6}{7}\) | |
| P1 | (dep P2) for start to process of solving pair of equations, eg eliminates one variable from the equations or removes fractions from both equations | |
| P1 | (dep P3) for complete process to solve equations to find \(g\) or \(r\) | |
| A1 | cao | |
| OR | ||
| P1 | for two of \(3x + 3\), \(4x + 2\) and \(7x + 5\) | |
| P1 | for \(\dfrac{3x + 3}{7x + 5} = \dfrac{6}{13}\) | |
| P1 | (dep P2) for removing fractions from the equation, eg \(13(3x + 3) = 6(7x + 5)\) or \(39x + 39 = 42x + 30\) | |
| P1 | (dep P3) for complete process to solve \(13(3x + 3) = 6(7x + 5)\) | |
| A1 | cao |