a)Completed table
jug of drinking water y cases of paper towels x
10 | 1000
30 | 50
42 | 20
b) Equation of the relationship is
40y + 16x <= 2000
c)The graph has y-intercept 50 and x-intercepts 125 and all regions below the line is solution.
How to interpret word problem
From the given information
Let y denote weight of a jug of drinking water
Let x denote weight of a case of paper towel.
If a jug of drinking water weighs 40 pounds
y jug of drinking water will weigh 40y.
if a paper towel weighs 16 pounds
x Paper towels will weigh 16x
But the maximum the truck can carry is 2000 pounds
Therefore, equation of the relationship is
40y + 16x <= 2000
2.5y + x <= 125
when y = 10
40(10) + 16x = 2000
400 + 16x = 2000
16x = 2000- 400
16x = 1600
x = 1600/16
= 1000
when x = 50
2.5y + 50 = 125
2.5y = 125-50
2.5y = 75
y = 75/2.5
y = 30
By comparing
when y = 42 and x = 20
40(42) + 16(20) = 2000
1680 + 3200 = 2000
2000 = 2000
Completed table
jug of drinking water y cases of paper towels x
10 | 1000
30 | 50
42 | 20
c) Given equation
40y + 16x <= 2000, find the equivalent by dividing through by 16
2.5y + x <= 125, plot the points
The graph has y-intercept 50 and x-intercepts 125 and all regions below the line is solution.