The Petersons have an applepressing machine that they use to

The Petersons have an apple-pressing machine that they use to make apple juice. The first pressing gets about 1/3 of the total juice in the aplles. Each succeeding pressing extracts about 1/3 of the remaining juice in the apples. How many pressings will it take to get at least 3/4 of the apples\' juice? how many pressings will it take to get at least 9/10 of the juice?

Solution

Let total juice in apples be x.

Juice obtained in first pressing = (1/3) x remaining juice = x-1/3 x = 2/3x

Juice obtained in second pressing = (1/3) (2/3) x= (2/9)x remaining juice = x - (1/3 x +2/9 x) = 4/9 x

Juice obtained in third pressing = (1/3) (4/9) x = (4/27) x remaining juice = x - (1/3 x +2/9 x + 4/27 x) = 9/27 x

In each pressing the qauntity of juice increases by 2/3.

So to get 3/4 x = 1/3 x * n * 2/3

3/4 * 3/2 * 3 =n

n = 27/8 = 3.37

so to get at leat 3.4 of the apples juice we need al least 4 pressings.

So to get 9/10 x = 1/3 x * n * 2/3

9/10 * 3/2 * 3 =n

n = 4.05