Answer: 192
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Step-by-step explanation
I'll show two methods to solving. There may be other approaches possible. Feel free to explore.
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Method 1
The ratio of flats to houses is 3:8
The ratio of houses to bungalows is 16:7
Double both parts of the 1st ratio to get 6:16. Notice the 16 matches with the other 16
We can then "glue", more or less, the ratios 6:16 and 16:7 to get the triple ratio 6:16:7
It means that for every 6 flats, there are 16 houses and 7 bungalows.
We can scale that ratio up to 6x:16x:7x for some positive whole number x.
There are 7x bungalows and we're told there are 224 bungalows.
So,
7x = 224
x = 224/7
x = 32
Then,
number of flats = 6x = 6*32 = 192 flats
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Method 2
The ratio of houses to bungalows is 16:7.
We'll use the idea there are 224 bungalows to find the number of houses.
houses/bungalows = 16/7
h/224 = 16/7
7h = 224*16 ...... cross multiplication
h = 224*16/7
h = 512
There are 512 houses.
We'll use that result and the first ratio to find the number of flats.
flats/houses = 3/8
f/512 = 3/8
8f = 512*3
f = 512*3/8
f = 192 flats