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Triana is on a 120-mile four-day bike ride. On the first day she travels 24 miles. She would like to travel equal amounts over the remaining three days. How far will she travel on each of those three days? Write and solve an equation of the form px+q=r. Then write a sentence to explain your answer.

User MrClean
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1 Answer

5 votes

Answer: 32 miles

Step-by-step explanation:

x = amount she travels on each of those three remaining days

3x = total amount traveled over those three remaining days

3x+24 = total amount traveled over the four days

3x+24 = 120 miles total

This equation is in the form px+q = r where:

  • p = 3
  • q = 24
  • r = 120

Let's solve for x. We follow PEMDAS in reverse to undo what's happening to x, so we can isolate it.

3x+24 = 120

3x+24-24 = 120-24 .... subtract 24 from both sides

3x = 96

3x/3 = 96/3 .... divide both sides by 3

x = 32

Triana must travel 32 miles per day for those remaining three days.

Doing so means she travels 3x = 3*32 = 96 miles over those three remaining days. Then add on those 24 miles traveled on the first day to get 96+24 = 120 miles total. This helps confirm the answer.

Another way to confirm the answer is to plug x = 32 into 3x+24 = 120. After simplifying both sides, you should get 120 = 120 which is a true statement.

User Falkb
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