Question

lesson 4: equations and their solutions
cool down
cool down: box of t-shirts
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.

1. name two possible solutions to the equation ( w = 250 + 132.5t ). what do the solutions mean in this situation?
2. 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 \(W = 250+132.5T\)

Let \(T = 0\), then \(W=250 + 132.5\times0=250\). This means when there are \(0\) T - shirts in the box, the weight of the box is \(250\) grams.
Let \(T = 2\), then \(W=250+132.5\times2=250 + 265=515\). This means when there are \(2\) T - shirts in the box, the weight of the box is \(515\) grams.

Step2: Solve \(2900=250 + 132.5T\)

Subtract \(250\) from both sides: \(2900-250=132.5T\), so \(2650 = 132.5T\).
Divide both sides by \(132.5\): \(T=\frac{2650}{132.5}=20\).

Answer:

1. Two possible solutions are \((T = 0,W = 250)\) and \((T = 2,W = 515)\). \((T = 0,W = 250)\) means the weight of the empty box (no T - shirts) is \(250\) grams. \((T = 2,W = 515)\) means the weight of the box with \(2\) T - shirts is \(515\) grams.
2. The solution \(T = 20\) of the equation \(2900=250 + 132.5T\) tells us that when the weight of the filled box is \(2900\) grams, there are \(20\) T - shirts in the box.