Question

cool down:
an empty shipping box weighs 250 grams. the box is then filled with t - shirts. each t - shirt weighs 132.5 grams. the equation ( w = 250+132.5t ) represents the relationship between the quantities in this situation, where ( w ) is the weight, in grams, of the filled box and ( t ) the number of shirts in the box.
a) name two possible solutions to the equation ( w = 250+132.5t ). what do the solutions mean in this situation?
b) consider the equation ( 2,900 = 250+132.50t ). in this situation, what does the solution to this equation tell us?

Explanation:

Step1: Find solutions for part a

Let's choose values for \(T\).

• When \(T = 0\):

\(W=250 + 132.5\times0=250\). This means when there are \(0\) T - shirts in the box, the weight of the box is \(250\) grams (the weight of the empty box).

• When \(T = 2\):

\(W=250+132.5\times2=250 + 265=515\). This means when there are \(2\) T - shirts in the box, the weight of the box is \(515\) grams.

Step2: Solve the equation for part b

We have the equation \(2900=250 + 132.5T\).
First, subtract \(250\) from both sides:
\(2900-250=132.5T\), so \(2650 = 132.5T\).
Then divide both sides by \(132.5\):
\(T=\frac{2650}{132.5}=20\).

Answer:

a) Two possible solutions are \((T = 0,W = 250)\) (empty box weight) and \((T = 2,W = 515)\) (box with 2 T - shirts weight).
b) The solution \(T = 20\) means that when the weight of the filled box \(W = 2900\) grams, there are \(20\) T - shirts in the box.