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Mr. M traveled 5 miles fewer than twice the number of miles on Tuesday as Monday. On Wednesday he traveled 40 more than the square of the number of miles traveled Monday. If the total miles traveled was 1,024, write an equation to represent the total miles traveled on Monday, Tuesday and Wednesday.

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Answer:

x² + 3x - 989 = 0 (where x is the number of miles traveled on Monday)

Step-by-step explanation:

Let x = number of miles traveled on Monday

Let y = number of miles traveled on Tuesday

Let z = number of miles traveled on Wednesday

Given:

  • Mr. M traveled 5 miles fewer than twice the number of miles on Tuesday as Monday

⇒ y = 2x - 5

Given:

  • On Wednesday he traveled 40 more than the square of the number of miles traveled Monday

⇒ z = x² + 40

Given:

  • Total miles traveled = 1024

⇒ x + y + z = 1024

Substitute  y = 2x - 5  and  z = x² + 40  into x + y + z = 1024:

⇒ x + 2x - 5 + x² + 40 = 1024

⇒ x² + 3x + 35 = 1024

⇒ x² + 3x - 989 = 0 (where x is the number of miles traveled on Monday)

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