Question

Gavin likes biking. He never misses a chance to go for a ride when the weather is nice. This week his goal is to bike about 65 total miles over four days. Each day, he wants to ride 1.5 times as far as he rode the day before. How far should he ride on each of the four days to reach his goal? If x is the number of miles Gavin bikes on the first day, write an expression for the distance he should bike on each of the following three days

Answer 1

How far should he ride on each of the four days to reach his goal?

1st day:
`8` miles

2nd day:
`12` miles

3rd day:
`18` miles

4th day:
`27` miles

Explanation: As the problem says,
`x` is the number of miles he rides on the first day. Let's start off with that.

1st day:
`x` miles

He want to ride 1.5 times as far as he rode the day before... no 1.5 more, but 1.5 times as far as he rode the day before; you would multiply 1.5 with the previous day's length.

2nd day:
`1.5x`

Then you multiply
`1.5` to
`1.5x` to get the third day's.

3rd day:
`2.25x`

4th day:
`3.375x`

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Phew! Gavin wants to ride a total of 65 miles over these four days, so if Gavin added all the miles of the four days, he should get 65...

1st+2nd+3rd+4th=65

`x+1.5x+2.25x+3.375x=65`

`8.125x=65`

`(8.125x)/(8.125)=(65)/(8.125)`

`x=8`

Yes! Now that we've got the hard part done... substitute 8 for ever single
`x`.

1st day:
`8` miles

2nd day:
`1.5(8)=12` miles

3rd day:
`2.25(8)=18` miles

4th day:
`3.375(8)=27` miles

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Checking my answer:

Just add the miles!

`8+12+18+27=65`

`65=65`

✓

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Hope that helps! :D