The number of marbles Chloe and Marcus had was in the ratio 7 : 3. Chloe then gave Marcus 24 marbles, and they had the same number each. How many marbles did Chloe have at first?
Chloe had 84 marbles at first.
Ans: 84
How to solve it
Draw the units: Chloe has 7 units and Marcus has 3 units.
Add them for the total: 7 units plus 3 units is 10 units.
The marbles only move across, so the total stays 10 units. Shared equally, that is 5 units each.
Find the units that moved: Chloe goes from 7 units to 5, so 7 minus 5 is 2 units, and that is 24 marbles.
Find 1 unit: 24 divided by 2 is 12. Chloe's 7 units are 7 times 12, which is 84 marbles.
The marbles only moved across. So the total is still 10 blue units, before and after. And Chloe's 7 units are 84 marbles.
Practice questions with worked solutions
Question 1 is free to try. The other 6 open in the free trial, each with its full working.
Question 1 of 7 · Intermediate · free to tryThe number of stickers in Album A to the number of stickers in Album B was…The number of stickers in Album…
The number of stickers in Album A to the number of stickers in Album B was in the ratio 5 : 3. 1/4 of the stickers in Album A were then moved to Album B. In the end Album B held 42 more stickers than Album A. How many stickers were there in the two albums altogether?
a quarter of Album A moves, so Album A must divide into quarters
Album A reads 5, and it has to reach a multiple of 4: 5 × 4 = 20
Album A : Album B = 5 : 3
× 4 = 20 : 12
before, 20 + 12 = 32 units
the stickers only changed album, so the end counts the same 32 units
stickers moved = 1/4 of 20 units = 5 units
Album A in the end = 20 units − 5 units = 15 units
Album B in the end = 12 units + 5 units = 17 units
Album B - Album A = 17 units − 15 units = 2 units
2 units = 42
1 unit = 42 ÷ 2 = 21
32 units = 32 × 21 = 672 stickers
Answer: 672
For parents
How do you solve constant total ratio questions in P6?
In these before-and-after word problems, something passes from one person or container to another, so nothing enters or leaves.
What your child learns here
In these before-and-after word problems, something passes from one person or container to another, so nothing enters or leaves. Your child learns to spot that the total is fixed and to give it the same number of units in both ratios.
Recognise a transfer: what one side loses, the other side gains.
Rewrite the before and after ratios so the total has the same number of units in both.
Find the units that moved, the value of 1 unit, and then any quantity asked for.
Applies equivalent ratios and the missing term in a pair of ratios to before-and-after problems.
Does the answer make sense?
Moving things from one album, jar or tank to another never changes the total, so your child's before and after amounts must add to the same number. Whoever gives cannot hand over more than they had, so a giver's amount at first must be bigger than the number moved.
How to practise these questions
Intermediate questions train using the unchanged total to compare the ratio before and after a transfer, whether a number or a fraction of one quantity is moved. The Challenge question holds the total fixed while items move between three containers, so three parts change at once. When the total that stays gets lost, read the written step-by-step solution.
Questions parents ask
What is a constant total ratio question? It is a before-and-after word problem where something only moves between two people or containers, so the total stays the same. Your child makes the total the same number of units in both ratios, then compares.
Is this kind of ratio question in the P6 syllabus? The syllabus lists equivalent ratios and finding the missing term in a pair of equivalent ratios. Before-and-after questions apply those outcomes to a story, and that is what this page teaches.
How do I know whether the total stays the same? Ask whether anything entered or left. If one side gives to the other and nothing else happens, the total is fixed. If both sides spend or receive, it is not, and a different method is needed.
