Question

1. A piece of power transmission equipment is being designed. The design includesa set of three different meshed gears with a total of 107 teeth between them. If thesecond gear has 13 more teeth than the first gear. The third gear has 15 more teeththan the second gear.How many teeth does the second gear have?

Answer 1

`x+y+z=107`

where x is the first, y the second and z the third

the second gear has 13 more teeth than the first gear

`x+13=y`

The third gear has 15 more teeth than the second gear

`y+15=z`

we need solve z form the third equation and solve x from the second equation an replace on the first

`\begin{gathered} z=y+15 \\ x=y-13 \end{gathered}`

replacing

`\begin{gathered} (y-13)+y+(y+15)=107 \\ y-13+y+y+15=107 \\ 3y+2=107 \\ 3y=105 \\ y=35 \end{gathered}`

so, the second gear have 35 teeth