Question P6 Constant total
Today’s problem — free all day, every step. Every day has one.
In a craft class, the ratio of Nadia's beads to Priya's beads was 4 : 1. After Nadia gave some of her beads to Priya, the ratio became 3 : 2. Together they had 150 beads throughout. How many beads did Nadia give to Priya?
Answer
Nadia gave Priya 30 beads. Check: at first they had 120 and 30 beads, so the ratio was 4 : 1 and the total was 150. After 30 beads moved, they had 90 and 60 beads, so the ratio was 3 : 2 and the total was still 150.
Money moves between two people, so their total never changes.
In this one. The beads only move between Nadia and Priya, so the same total of 150 can be split using each ratio in turn.
One person gives, sells or loses an amount to the other, and nobody outside the two people gains or loses anything.
Children draw different totals before and after, or forget that moving an amount from one person to the other changes the gap between them by twice that amount.
Worked examples of all 33 patterns and skills, in a booklet you can print.