Hello!

Denote the number of miles ridden as `x.` Then $0.65 per mile means that the price will be `0.65*x` for a mileage and the total price including flat rate will be

`0.65*x+1.75.`

If Sheena want to spend all her $10, we obtain a linear equation

`0.65*x+1.75=10.`

This is the answer.

It is simple to solve it: subtract 1.75 from the both sides and obtain

`0.65*x=10-1.75=8.25,`

then divide both sides by 0.65 and obtain the solution

`x=8.25/0.65 approx 12.7` (miles).

Actually, the text of the problem gives us a linear *inequality*,

`0.65*x+1.75lt=10,`

because "Sheena has *no more* *than $10* to spend on a ride."

The solution for this inequality is `xlt=12.7.`

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