Question

Four balls of wool will make eight knitted caps. How many balls of wool will Malcolm need if he wants to make six caps?

Answer 1

3

Explanation:

Set up a ratio
let 4 balls be the numerator of the first fraction
let 8 caps be the denominator of the first fraction
Let x balls be the numerator of the second fraction
Let 6 caps be the denominator of the second fraction

Set the two fractions equal to each other and solve.

`4/8 = x/6`

Multiply both sides by 6

`6 xx (4/8) = 6 xx ( x/6)`

The 6s divide out on the right side giving

`24/8 = x` so

`3 = x`

Answer 2

`3` balls of wool

Explanation:

You can determine how many caps can be made from one ball of wool.

`8` caps are made from `4` balls of wool.
`:. 2` caps can be made from `1` ball of wool.

Each cap requires `1/2` ball.

To make `6` caps:

`6xx 1/2= 3` balls of wool.

You can also use direct proportion:

`8/4 = 6/x" "(larr "caps")/(larr"balls")`

`x = 3` balls of wool