Question

running the table shows the lengths of several routes hector can take when he goes running. route length (miles) a 4.1 b 2.85 c 11.9 d 5.76 e 3.28 complete the expressions so hector will get as close to his goal as possible for each week given. week 1: 3b + 2 goal: total of 20 miles week 2: 4e + 3 goal: total of 25 miles

Explanation:

Step1: Calculate the value of 3B

Given B = 2.85, then 3B=3×2.85 = 8.55.

Step2: Let the unknown part be x. Set up an equation for Week 1

We know the goal is 20 miles. So, 8.55 + 2x=20. Solving for x, we first subtract 8.55 from both sides: 2x=20 - 8.55=11.45. Then x = 11.45÷2 = 5.725. Since D = 5.76 which is closest to 5.725 among the given routes, it is the correct choice for Week 1.

Step3: Calculate the value of 4E

Given E = 3.28, then 4E=4×3.28 = 13.12.

Step4: Let the unknown part be y. Set up an equation for Week 2

The goal is 25 miles. So, 13.12+3y = 25. First, subtract 13.12 from both sides: 3y=25 - 13.12 = 11.88. Then y=11.88÷3 = 3.96. Since no route exactly matches 3.96, but we assume we are still working with the given routes and E = 3.28 is the closest - related value among the options provided (as we are using combinations of the given routes), we assume the second - blank should be E again for Week 2.

Answer:

Week 1: D
Week 2: E