Minus' Solution to

Knitting Knumbers
Posted Weeks of May 18 - 31, 1998

If it takes 4 red balls to knit one kitty sweater, Kay will need 1 1/3 red balls of yarn to make 1/3 of the sweater red.

Since 3 yellow balls are equivalent to one red ball, it will take 4 yellow balls to make 1/3 of the sweater.

Since 2 yellow balls are equivalent to one blue ball, it will take 2 blue balls to make 1/3 of the sweater.

Which means Kay will need a total 7 1/3 yarn balls to make a sweater with an even pattern of red, yellow and blue.

Taryn Chua, from Methodist Ladies' College, struts her stuff by solving this problem using algebra. Way to go, Taryn. That's using your smarts to feed Minus!

Dear Sir Minus(who has recently been knighted),

let the number of blue balls = b
let the number of red balls = r
let the number of yellow balls = y

If yellow balls have only half as much yarn as the blue, then: 2y = b
If red balls have three times as much yarn as the yellow, then: r = 3y

And I know that 4 red balls make one sweater, thus: 4r = one sweater So I know that to make an even pattern of red, yellow, and blue I have to use 1 and 1/3 red-sized balls of each colour.

For red yarn, this will simply be 1 1/3 red balls. For yellow yarn, I know that 3y = r and this means that:
1 red ball = 3 yellow balls
1 1/3 red balls = 3 * 1 1/3 yellow balls
1 1/3 red balls = 4 yellow balls

So I know for yellow yarn I will need 4 balls. For blue yarn, I know that 2y = b and I know already that 4 yellow balls = 1 1/3 red balls so this means:
2 yellow balls = 1 blue ball
4 yellow balls = 2 blue balls
So I know for blue yarn I will need 2 balls.

Kay Kat needs 1 1/3 red balls, 4 yellow balls, 2 blue balls and this is a total of 7 1/3 balls of yarn altogether, except I think the cat needs a much more *suave* name like GARFIELD!

You will need 1 1/3 balls of red yarn, 4 balls of yellow yarn, and 2 balls of blue yarn to make one sweater.

Since it takes four balls of red to make one  red sweater, it would take 12 balls of yarn to make a yellow sweater  (3 times as much) and 6 balls of yarn to make a blue sweater(1/2 as much as yellow). With 4 red + 12 yellow + 6 blue balls of yarn, you would make 3 sweaters. Take 1/3 of that and you get the above answer.

yellow: 1/3 of red, 1/2 of blue

4 red balls make sweater
3 * 4 = 12 yellow balls to make sweater
12/2= 6 blue balls make sweater

1/3 of each

12/3 = 4 yellow balls
6/3 = 2 blue balls
4/3 = 1 and a 3rd red balls

7 1/3 balls in total

yellow 1/3 of red blue is 2/3 of red

1 1/3 balls of red

4 balls of yellow

2 balls of blue

7 1/3 balls of yarn.