Question

Ok so I have three questions:

1.
Patty's Pet Company charges $0.55 per pound to ship pet supplies.

Part A: Write an equation to determine the total cost, c, to ship p pounds of pet supplies. Use your equation to determine the cost of shipping 2 pounds of pet supplies.

Part B: If the company reduces the cost to ship pet supplies by 0.05 per pound, write an equation to determine the total cost, c, to ship p pounds of pet supplies with the reduced cost.

2.
Jason left a bin outside in his garden to collect rainwater. He notices that 1/5 gallon of water fills 2/3 of the bin. Write and solve an equation to find the amount of water that will fill the entire bin. Show your work. Explain your answer in words.

3.
The price of a video game is $32.99 before tax. Andre bought the video game for 20% off. He then paid 8% sales tax on the discounted price.

Part A: How much did Andre pay in sales tax? Show all work and steps in your solution.

Part B: What is the total amount that Andre paid for the video game? Show all work and steps in your solution.

Sorry I’m a noob :/

Answer 1

In order to create an equation for #1 Part A, you have to be able to calculate the total cost (c) for shipping pounds (p) at $0.55 per pound.
\[c = 0.55p\]
For Part B we simply subtract $0.05 from $0.55
\[c = (0.55 - 0.05)p\]
You can simplify this.

For #2 they essentially tell us:
\[\frac{ 1 }{ 5 }g =\frac{ 2 }{ 3}b\]
1/5 of a gallon fills 2/3 of a bin, since they want us to solve for how much water (in gallons) fills a bin, we solve for b. In order to do so, we do the algebraic process of isolating the variable
\[\frac{ 3 }{ 2 } \times \frac{ 1 }{ 5 }g =\frac{ 2 }{ 3}b \times \frac{ 3 }{ 2 }\]
In accordance with the Multiplication Property of Equality, we multiply both sides by the same #. We do this to get b alone on one side, obtaining..
\[\frac{ 3 }{ 10}g = \frac{ 6 }{ 6}b \rightarrow \frac{ 3 }{ 10}g = b\]

Answer 2

For #3 you must start by obtaining 20% of $32.99, subtracting it from $32.99, then obtaining 8% of the discounted price (the value obtained after tacking off 20% of $32.99).
Let p = price paid in sales tax
\[p = (32.99 - 32.99(0.20))0.08\]