Answer:
- (a) most flats/cottage: Village Y
- (b) most houses/cottage: Village X
Explanation:
Given numbers of cottages, flats, and houses in villages X, Y, and Z, you want to identify (a) the village with the most flats for each cottage, and (b) the village with the most houses for each cottage.
Ratios
We can multiply the numbers for Village X by 4, and the numbers for Village Y by 10 to put the ratios into a form we can compare:
cottages : flats : houses
X — 5 : 18 : 27 = 20 : 72 : 108
Y — 2 : 12 : 8 = 20 : 120 : 80
Z — 20 : 3 : 2 . . . . . . . . . . . . . . . . already has 20 villages
a) Most flats
The village with the most flats in the rewritten ratios is village Y.
Village Y has the most flats for each cottage.
b) Most houses
The village with the most houses in the rewritten ratios is village X.
Village X has the most houses for each cottage.
__
Additional comment
When comparing to cottages, as here, it is convenient to use the same number for cottages in each of the ratios. Rather than divide each line by the number of cottages in the village, we elected to multiply each line by a number that would make the cottage numbers all the same. We find this latter approach works better for mental arithmetic.
When figuring "flats per cottage", we usually think in terms of a "unit rate", where the denominator is 1. For comparison purposes, the "twenty rate" works just as well, where we're comparing to 20 cottages.
If you were doing a larger table, or starting with numbers other than 2, 5, and 20 (which lend themselves to mental arithmetic), you might consider having a spreadsheet do the arithmetic of dividing by the numbers of cottages.
<95141404393>