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a part has broken on a machine and needs to be replaced .The replacement part must be between 71/16 cm and 71/6 cm long in order to fit.

a part has broken on a machine and needs to be replaced .The replacement part must-example-1

1 Answer

2 votes

Answer:

Yes, it will fit

Explanation:

The red part of the detail is
4(7)/(9)\ cm long, the yellow part is
2(1)/(3)\ cm long.

In order to fit the conditions, both parts together should be no longer than
7(1)/(6)\ cm and no less than
7(1)/(18)\ cm.

Find the combined length of red and yellow parts:


4(7)/(9)+2(1)/(3)\\ \\=(4+2)+\left((7)/(9)+(1)/(3)\right)\\ \\=6+\left((7)/(9)+(3)/(9)\right)\\ \\=6+(10)/(9)\\ \\=6+1(1)/(9)\\ \\=7(1)/(9)\ cm

Note that


7(1)/(9)=7(2)/(18)>7(1)/(18),

so the combined length is no less than
7(1)/(18)\ cm

and


7(1)/(9)=7(2)/(18)\\ \\7(1)/(6)=7(3)/(18)\\ \\7(2)/(18)<7(3)/(1)8\Rightarrow 7(1)/(9)<7(1)/(6),

so the combined length is no more than
7(1)/(6)\ cm

User Collin Green
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