Question

Five road bikes and four mountain bikes will cost you $6,400. One of each will cost you $1,400. What does a road bike cost?

Answer 1

Road bike costs: `$800`

Explanation:

Road bikes: `x`
Mountain bikes: `y`

`5x+4y=6400`
`x+y=1400`

We have a System of Equations problem here, so we will solve along those lines.

Isolating variable `x` in the second equation, we get
`x=1400-y` which we can replace for `x` in the first equation...
`\therefore5(1400-y)+4y=6400`

Now, solving for `y`...
`7000-5y+4y=6400`
`7000-y=6400`
`y=7000-6400`
`y=600`

We have `y`, now plug that in to solve for `x`...
`x=1400-y`
`x=1400-600=800`

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`x=800,y=600`
A road bike costs `$800` and a mountain bike costs `$600`.