Chloe had 5 times as many marbles as Marcus. Chloe gave Marcus 24 marbles. Then they had the same number of marbles. How many marbles did Chloe have at first?
Total = 5 units + 1 unit = 6 units
Each child in the end = 6 units ÷ 2 = 3 units
Units Chloe gave = 5 units − 3 units = 2 units
2 units = 24
1 unit = 24 ÷ 2 = 12
Chloe at first = 5 × 12 = 60
Chloe had 60 marbles at first.
Ans: 60
Practice questions with worked solutions
Question 1 is free to try. The other 4 open in the free trial, each with its full working.
Question 1 of 5 · Intermediate · free to tryTwo boxes contain 315 cards altogether. After 42 cards move from Box A to…Two boxes contain 315 cards…
Two boxes contain 315 cards altogether. After 42 cards move from Box A to Box B, Box B has twice as many cards as Box A. How many cards were in Box B at first?
How can I explain P4 unchanged total questions to my child?
Your child recognises that transferring items between two people changes their individual amounts but preserves their combined total.
What your child learns here
Your child recognises that transferring items between two people changes their individual amounts but preserves their combined total. This is a problem-solving application of whole-number operations within the Primary 4 course. Keeping the before and after amounts separate helps your child use the unchanged total without assuming either person's amount is fixed.
Identify the two quantities included in the total and establish that the transferred items remain within that pair rather than entering or leaving it.
Subtract the transfer from the giver's amount and add the same transfer to the receiver's amount when calculating the after state.
Use the shared total with a before or after relationship, such as equal final amounts, to recover an unknown quantity.
Recognise that a transfer from the larger amount to the smaller reduces their difference by twice the transferred amount until they become equal.
Reverse the transfer when the question gives final amounts but asks for an original amount, keeping track of who gave and who received.
Does the answer make sense?
Add the two amounts before the transfer and add the two amounts after it; those totals must be equal when nothing enters or leaves the pair. Your child can also check that the giver's decrease exactly matches the receiver's increase.
How to practise these questions
The Intermediate questions recover an original receiver's amount, use the way a transfer changes a difference and work from an equal starting state to a later comparison. The Challenge question extends the same total-preserving idea to three trays and two successive transfers. This selection has no Basic band. Have your child describe each transfer in order, naming the giver and receiver before calculating. In the three-quantity question, a middle tray both receives and gives, so its net change combines two actions. Check the combined total across all the quantities involved, then reverse the transfers to confirm any original amount found from the final state.
Questions parents ask
Why does a transfer change the difference twice? The larger amount decreases while the smaller amount increases by the same transfer. Both changes close the original gap. If the transfer makes the amounts equal, the starting difference is twice the transferred amount, so transferring the entire starting difference would go too far.
Does giving something away always leave the total unchanged? It depends on whose total is being considered. A transfer between the two people in the problem preserves their combined total. If items are given to someone outside that pair, their combined amount falls. Ask your child to identify the group before naming what stays unchanged.
How can my child find an amount from before the transfer? Reverse the stated change from the known final amount. Add the transfer back to the giver, or subtract it from the receiver. Your child can then run the transfer forwards again and check that both the final relationship and the combined total are restored.
