Chapter ISG, Problem 5.1.1.11P

a.

To determine

To write an inequality that expresses the constraints of the situation

Answer to Problem 5.1.1.11P

  $2x+5\ge 20$

Explanation of Solution

Given information:

M rode his bike 5 miles more than B

Altogether they rode at least 20 miles

Calculation:

Let B rode his bike to at least $x$ miles

Then M will ride his bike to at least $x+5$ miles

They together rode at least 12 miles which means:-

  $x+x+5\ge 20$

Solving it further

  $2x+5\ge 20$

Subtracting 5 from both sides of inequality

  $2x+5-5\ge 20-5$

The inequality can be expressed as

  $2x\ge 15$

b.

To determine

To solve the inequality to express the number of miles each person rode

Answer to Problem 5.1.1.11P

B rode at least 7.5 miles

M rode at least 12.5 miles

Explanation of Solution

Given information:

M rode his bike 5 miles more than B

Altogether they rode at least 20 miles

Calculation:

Substituting the value of inequality from part a

  $x\ge 7.5$

B rode At least $x$ miles

Substituting the value of $x$

Therefore B rode At least 7.5 miles

M rode $x+5$ miles

Substituting the value of $x$

(7.5 + 5) miles

Calculating the final answer

M rode At least 12.5 miles