Question P6 Everything changed
Today’s problem — free all day, every step. Every day has one.
The ratio of Emma’s savings to Lily’s savings was 2:1. After Emma saved $60 and Lily spent $30, the new ratio became 4:1. How much money did Emma have at first?
See all 9 steps
MathBrush is being tested with a few parent groups, and every solution on the site is open to them — one household, all children. If you were given a code, it goes in once and this device remembers it.
I have a code → See a free one like it
65 worked examples are free without a code, two from every pattern. No account, either way.
Both amounts change, so no total and no gap stays fixed.
In this one. Both quantities changed, so a unit of the ratio at first and a part of the ratio at the end are different sizes — swap every unit for 1 part + 30 (Lily's change) and Emma's whole equation becomes one in parts alone.
Both people in a ratio change by different amounts, with words like 'joined' or 'saved more' for one and 'left' or 'spent' for the other.
Children look for a fixed total or a fixed gap out of habit. Neither is fixed here, so only the ratio at the end can give the size of a share.
Worked examples of all 33 patterns and skills, in a booklet you can print.