Today Puzzle #560
Puzzle No. 561鈥� Wednesday 5 September
37 years ago James was twice as old as Sarah. 19 years ago Sarah was three quarters of James’s age. How old are James and Sarah?
Today’s #PuzzleForToday has been set by Dr Kit Yates is the author of The Maths of Life and Death - how mathematics plays a crucial role in helping us navigate the real world.
Click here for the answer
Let’s call James’s age J and Sarah’s S.
The first statement tells us that
2(S-37)=J-37,
which we can rearrange to give James’s age in terms of Sarah’s:
J = 2S-37.
The second statement tells us that
S-19 = 3/4 * (J-19),
which we can rearrange to give
4S=3J+19.
Then we can substitute in for James’s age from the first rearranged expression and simplify to give
S=46.
Using the first rearranged expression we can find
J=55.
Sarah is 46 while James is 55.
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