



 
Hi Kenneth, First let me show you how I would solve this problem and then try to explain why the "formula you used" gives the same solution.
If you have half as many carpenters they can only build half as many houses in 10 days. Hence
If these 2 carpenters only have 5 days they can only build half as many houses. Thus
But if they have 15 days then can build 3 times as many houses so
Look at the number of houses in the 4 statements. The number of houses started at 8, then I multiplies by $\large \frac12.$ I then multiplied by $\large \frac12$ again and finally I multiplies by $3.$ Thus my calculation was \[8 \times \frac12 \times \frac12 \times3.\] But $\large \frac24 = \frac12$ and $\large \frac{15}{10} = \frac12 \times 3.$ so my calculation can be written \[8 \times \frac24 \times \frac{15}{10} = \frac{8 \times 2 \times 15}{4 \times 10}\] Penny  


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