The total stays the same

The number of marbles Chloe and Marcus had was in the ratio 7 to 3. Chloe then gave Marcus 24 marbles, and they had the same number each. How many marbles did Chloe have at first? Try it first. Pause if you like. Draw what we know. Chloe has 7 blue units. Marcus has 3 blue units. Now put the two bars end to end. Altogether, that's 10 blue units. 7 units and 3 units make 10 units. Now Chloe gives Marcus 24 marbles. Some of Chloe's marbles move across to Marcus. We don't know how many units that is yet. Nothing was added, and nothing was thrown away. So the total is still 10 blue units. Afterwards, they have the same number each. So those 10 units split into two equal shares. 10 units divided by 2 is 5 units each. So Chloe's last 2 blue units cross over to Marcus. Now look at Chloe. She started with 7 blue units, and she's left with 5. 7 units minus 5 units is 2 units. And those 2 units are the 24 marbles. Now share that 24 between the 2 units. 24 divided by 2 is 12. So 1 unit is 12 marbles. So Chloe had 7 units at first. And 1 unit is 12 marbles. 7 times 12 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.