Ratio (Maths 1 Shinglee pg243) Example

The ratio of the number of apples to oranges in Stall A and Stall B are 2:5 and 5:9 respectively. If the total number of fruits in Stall A is twice that in Stall B,
(a) find the ratio of the number of apples in Stall A to the number of apples in Stall B;
(b) find the number of oranges left in Stall A after 84 oranges are sold from Stall A and the ratio of apples to oranges becomes 3:4 in Stall A.

This example in the Sec 1 text was solved using Algebra. Here we try the units method:

(a)
Stall A Apples:Oranges = 2:5 (total 7 units) or 8:20 (28 units - fruits in Stall A double Stall B's)
Stall B Apples:Oranges = 5:9 (total 14 units)

Ratio of Apples (Stall A) to Apples (Stall B) = 8:5

(b)
Before : Stall A A:O = 2:5 or 6:15 (A stays same, so make the same units before and after)
After: A:O = 3:4 or 6:8
Oranges -7 units or -84
7 units = 84, 1 unit = 12

Oranges (after) = 8 units or 8x12 =96