Answer:
How far should he ride on each of the four days to reach his goal?
1st day: [tex]8[/tex] miles
2nd day: [tex]12[/tex] miles
3rd day: [tex]18[/tex] miles
4th day: [tex]27[/tex] miles
Step-by-step explanation: As the problem says, [tex]x[/tex] is the number of miles he rides on the first day. Let's start off with that.
1st day: [tex]x[/tex] 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: [tex]1.5x[/tex]
Then you multiply [tex]1.5[/tex] to [tex]1.5x[/tex] to get the third day's.
3rd day: [tex]2.25x[/tex]
4th day: [tex]3.375x[/tex]
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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
[tex]x+1.5x+2.25x+3.375x=65[/tex]
[tex]8.125x=65[/tex]
[tex]\frac{8.125x}{8.125}=\frac{65}{8.125}[/tex]
[tex]x=8[/tex]
Yes! Now that we've got the hard part done... substitute 8 for ever single [tex]x[/tex].
1st day: [tex]8[/tex] miles
2nd day: [tex]1.5(8)=12[/tex] miles
3rd day: [tex]2.25(8)=18[/tex] miles
4th day: [tex]3.375(8)=27[/tex] miles
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Checking my answer:
Just add the miles!
[tex]8+12+18+27=65[/tex]
[tex]65=65[/tex]
✓
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Hope that helps! :D
