Chapter 5.3, Problem 46MS

Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming them, of expressing infinitely many relationships and connections clearly and succinctly, and of uncovering pattern and structure.

Box o’ knots (H). There is a box of knotted bunches of string in your math instructor’s classroom. The number of trefoil knots in the box is x and the number of figure-eight knots is y. You take all the knots out of the box and display them so each looks like the trefoil or figure-eight knot illustrated in Mindscape 20. If there are a total of 21 knots and 74 crossings, how many knots are there of each type?