PartBecause his goal is to bike 65 miles over four days, what equation can be used to find the number of miles he should bike on the first day, X? Donot combine like terms.BFont SizeA- A

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31-10-2022
Mathematics

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PartBecause his goal is to bike 65 miles over four days, what equation can be used to find the number of miles he should bike on the first day, X? Donot combine like terms.BFont SizeA- A

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PalmerG541311 PalmerG541311 · Answer 1 · 2022-10-31T02:26:42-04:00

The biker needs to travel 65mi in four days and each day he needs to ride 1.5 the distance he did the day before.

In Part A you found that:

Day 1: 8 mi

Day 2: 1.5 (8mi)=12mi

Day 3: 1.5(12mi)=18mi

Day 4: 1.5(18mi)=27mi

This was just a recompilation of our previous results

Regarding part B

So, if x represents the distance traveled during the first day, once we add up each day we obtain the next expression:

[tex]x+1.5x+1.5(1.5x)+1.5(1.5(1.5x))[/tex]

Notice that the first term corresponds to the distance he bikes on the first day, the second term corresponds to the second day, and so on.

[tex]x+1.5x+1.5(1.5x)+1.5(1.5(1.5x))=x+1.5x+2.25x+3.375x=d[/tex]

d represents the total distance during the 4 days

And remember, do not combine like terms!

This represents how much distance he will ride during the 4 days given the first-day distance

And, as you found in part A, if x=8, then 8.125(8)=65. So, our result is consistent.

Regarding Part C

Now, as our goal is to ride during 65mi, we only need to do d=65mi, giving us:

[tex]x+1.5x+1.5(1.5x)+1.5(1.5(1.5x))=x+1.5x+2.25x+3.375x=65[/tex]

Regarding part D:

First, let's remember what 'like terms' mean:

An easy example of like terms is the next set: x, 2x, -7x

Notice that all of them share the term x, so they are 'like terms'

Going back to part C, we have that our final expression is:

[tex]x+1.5x+2.25x+3.375x=65[/tex]

As you can see, the left side of the equation contains terms that involve the x-factor, so all the terms on the left side are 'like terms' involving x

[tex]x,1.5x,2.25x,3.375x[/tex]