Question

name: jaydeci 1.11 formative assessment (a)
suppose that you decide to participate in a charity walkathon to raise money for your cause. some people decide to donate a fixed amount, while others agree to donate a little money for every mile you walk. before the event starts, you raised $25, and you have been pledged $1.50 for each mile you walk. the function defined by ( d(w)=1.5w + 25 ) can be used to relate the miles you walk, ( w ), and the amount of money donated to you in dollars, ( d(w) ).
(a) evaluate ( d(3) ), and explain what it means in the context of the problem.
(b) while you were walking, you lost track of the number of miles you had walked. at the end of the event, an organizer tells you that you raised $40 through your walk. how many miles did you walk?

Explanation:

Step1: Evaluate \(d(3)\)

Substitute \(w = 3\) into \(d(w)=1.5w + 25\).
\(d(3)=1.5\times3+25\)
\(d(3)=4.5 + 25\)
\(d(3)=29.5\)

Step2: Interpret \(d(3)\)

In the context of the problem, \(w\) is the number of miles walked. When \(w = 3\) (walked 3 miles), \(d(3)\) represents the total money donated. So, it means that when you walk 3 miles, the total amount of money donated to you is \(\$29.5\).

Step3: Solve for \(w\) when \(d(w)=40\)

Set \(d(w)=40\) in the equation \(d(w)=1.5w + 25\).
\(40=1.5w + 25\)
Subtract 25 from both sides: \(40 - 25=1.5w\)
\(15 = 1.5w\)
Divide both sides by 1.5: \(w=\frac{15}{1.5}\)
\(w = 10\)

Answer:

(a) \(d(3)=29.5\), which means when you walk 3 miles, the total donation is \(\$29.5\).
(b) \(10\) miles.