Question

1. boxes of postcards are being shipped. the total shipping weight is proportional to the number of boxes shipped. its known that 8 boxes weigh 30 pounds.

(a) using the ratio of pounds to boxes given, finish the table below.

boxes	pounds
4
8	30
12
16

plot this table as three additional (x, y) pairs. draw a line through the plotted points.
(b) what is the ratio of weight to boxes? express as a unit rate with appropriate units.
(c) what (x, y) point on the graph does the answer to (b) correspond to? plot it.
(d) a shipment contained 960 pounds. let b equal the number of boxes shipped. solve a proportion for the value of b.
n-gen math™ 7, unit 3 - proportional relationships - lesson 7
emathinstruction, red hook, ny 12571, © 2020

Explanation:

Step1: Find unit weight per box

$\text{Unit rate} = \frac{30}{8} = 3.75$ pounds per box

Step2: Fill table for (a)

For 4 boxes: $4 \times 3.75 = 15$ pounds
For 12 boxes: $12 \times 3.75 = 45$ pounds
For 16 boxes: $16 \times 3.75 = 60$ pounds
(Plot points (4,15), (12,45), (16,60) and draw a line through all points including (0,0) and (8,30))

Step3: Answer (b) unit rate

The ratio simplifies to $\frac{30}{8} = 3.75$ pounds/box

Step4: Match point for (c)

Unit rate corresponds to 1 box, 3.75 pounds: $(1, 3.75)$

Step5: Solve proportion for (d)

Set up proportion: $\frac{30}{8} = \frac{960}{b}$
Cross multiply: $30b = 960 \times 8$
Calculate: $30b = 7680$
Solve for $b$: $b = \frac{7680}{30} = 256$

Answer:

(a) Completed table:

Boxes	Pounds
4	15
8	30
12	45
16	60

(Plot the points (4,15), (12,45), (16,60) and draw a straight line through all plotted points)

(b) 3.75 pounds per box

(c) $(1, 3.75)$ (plot this point on the graph)

(d) 256