Stage 8 - Q1 - 2 marks
Share 60 in the ratio \(5:7\).
Hint
There are twelve parts.
Stage 8 - Q2 - 2 marks
Share 96 in the ratio \(1:2:5\).
Hint
First add all three ratio terms.
Stage 8 - Q3 - 2 marks
Three teams share 105 points in the ratio \(2:3:2\). Find each share.
Hint
The first and third teams receive equal shares.
Stage 8 - Q4 - 2 marks
The angles in a triangle are in the ratio \(2:3:4\). Find all three angles.
Hint
The total angle is 180 degrees.
Stage 8 - Q5 - 3 marks
Two people share money in the ratio \(3:7\). The smaller share is 18 USD. Find the larger share and the total.
Hint
Use the known share to find one part.
Stage 8 - Q6 - 3 marks
Two prize shares are in the ratio \(4:9\) and differ by 35 USD. Find both shares.
Hint
Match the difference to the difference of the ratio terms.
Stage 8 - Q7 - 4 marks
Three workers spend 3, 4 and 5 hours on a job. They share 156 USD in proportion to their hours. How much more does the last worker receive than the first?
Hint
The difference between their hours is two ratio parts.
Stage 8 - Q8 - 4 marks
Three people can share 180 USD in the ratio of their ages, \(11:13:16\), or heights, \(140:150:160\). Which option gives the middle person more, and by how much?
Hint
Compare the middle fraction of each whole.
Stage 8 - Q9 - 5 marks
A, B and C share 240 USD in the ratio \(3:4:5\). A then gives C 12 USD. Find their new ratio in simplest form.
Hint
A transfer changes two shares but preserves their total.
Stage 8 - Q10 - 5 marks
Children aged 4, 7 and 9 share 260 USD in the ratio of their ages. Two years later they share the same total using their new ages. Show that the oldest receives less, and find the decrease.
Hint
All three ages change, so the denominator changes too.