Ask Uncle Colin: A Rational Mess | Colin

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can.

Dear Uncle Colin, I’ve got a ratios question, and I don’t understand the solution.

The question is: Three numbers, $x$, $y$, and $z$, have a sum of 871. The ratio $x:y$ is 4:5 and the ratio $y:z$ is 3:8. What is the value of $y$?

Their solution is to say the ratio $x:y = 4:5 = \left(4\times\frac{3}{5}\right):\left(5\times\frac{3}{5}\right) =…

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