### 2-6: Writing Problem Situations

#### Part 1

Example Using Equations to Represent Real-World Problems

Can you use the equation 4 = 10x + 0.5 to represent the problem? Explain your reasoning.

• a. You have 4 cups of trail mix. You eat 0.5 cup of the trail mix and divide the rest into 10 equal portions. How much trail mix is in each portion?

• b. Renting a bike costs \$10 for the first hour and \$4 for every 0.5 hour after the first hour. Your total rental cost is \$10. For how many hours did you rent the bike?

• c. You have 0.5 yard of red ribbon and 10 pieces of blue ribbon of equal length. You have 4 yards of ribbon in all. How long is each piece of blue ribbon?

Solution

• a. Yes, you can use the equation 4 = 10x + 0.5 to represent the situation. • b. No, you cannot use the equation 4 = 10x + 0.5 to represent the situation. For this problem, 0.5 is a unit of time for the variable. So, 0.5 should not appear in the equation. An equation that could represent this problem is 10 = 10 + 4x, where x is the number of half-hours after the first hour.

• c. Yes, you can use the equation 4 = 10x + 0.5 to represent the situation. End ofPage 79