Stage 9 - Q1 - 2 marks
\(A:B=3:6\) and \(B-A=30\). Find \(A\) and \(B\).
Hint
Subtract the ratio terms before dividing the given difference.
Stage 9 - Q2 - 2 marks
\(A:B=4:6\) and \(B-A=10\). Find \(A\) and \(B\).
Hint
Subtract the ratio terms before dividing the given difference.
Stage 9 - Q3 - 3 marks
Three shares are in ratio \(5:9:11\). Largest minus smallest is 66. Find the total.
Hint
The given difference is not the total.
Stage 9 - Q4 - 3 marks
Two positive numbers have ratio \(2:5\). One is 60. Find both possible values of the other.
Hint
Solve once with the known value in each position.
Stage 9 - Q5 - 2 marks
Two masses have ratio \(3:5\) and differ by 2.4 kg. Find both masses.
Hint
The mass difference matches the difference of the ratio terms.
Stage 9 - Q6 - 4 marks
A triangle has largest angle \(85^\circ\). The other angles differ by \(25^\circ\). Find the ratio of all three angles, smallest first.
Hint
If the smaller angle is x, the next is x plus the difference.
Stage 9 - Q7 - 3 marks
Two positive numbers have ratio \(5:8\). One is 80. Find both possible values of the other.
Hint
Solve once with the known value in each position.
Stage 9 - Q8 - 3 marks
Three shares are in ratio \(2:4:6\). Largest minus smallest is 32. Find the total.
Hint
The given difference is not the total.
Stage 9 - Q9 - 4 marks
A triangle has largest angle \(90^\circ\). The other angles differ by \(15^\circ\). Find the ratio of all three angles, smallest first.
Hint
If the smaller angle is x, the next is x plus the difference.
Stage 9 - Q10 - 5 marks
Two boxes contain counters in ratio \(4:7\). Moving 9 counters from the larger box to the smaller makes the counts equal. Find the original counts.
Hint
The original difference is twice the transferred amount.