Complete question:
A postage company delivers parcels which are in the shape of a cuboid. The length of every side of the parcel must be a whole number of centimeters. The price in cents is determined by multiplying the weight of the parcel (to the nearest kilogram) by 30 and then adding on 20 times the length of the longest side of the parcel.
What is the largest parcel that weighs 5KG could be if the price for sending it is less than three dollars
Answer:
7cm long
Step-by-step explanation:
Given
Let
[tex]w = weight[/tex]
[tex]l = longest\ side[/tex]
[tex]p = price[/tex] --- in cents
From the question, p is calculated as:
[tex]p = 30w + 20l[/tex]
Required
Calculate the largest parcel when weight = 5 kg and price < $3
Convert price to cents
[tex]p <\$3[/tex]
[tex]p <3*100\ cents[/tex]
[tex]p <300\ cents[/tex]
The formula: [tex]p = 30w + 20l[/tex] becomes
[tex]30 * 5 + 20 * l < 300[/tex]
[tex]150 + 20 * l < 300[/tex]
Collect like terms
[tex]20 * l < 300 - 150[/tex]
[tex]20 * l < 150[/tex]
Divide both sides by 20
[tex]l < 7.5cm[/tex]
Since the length must be in whole numbers, then the largest parcel is 7cm long
