A store sells pens and note pads in packages. The price of a package of 8 pens and 3 notepads is 4.25. The price of a package of 15 pens and 10 notepads is 11.25. The store is running a sale on a package of 1 pen and 1 notepad for 1.10. Is the sale price a better deal than the other packages? Show your work.
Need help!
Well, let's break it down, my friend!
Package 1: 8 pens and 3 notepads for $4.25.
Package 2: 15 pens and 10 notepads for $11.25.
Sale Package: 1 pen and 1 notepad for $1.10.
First, let's figure out the cost of each pen and notepad separately in Package 1:
Cost of 1 pen in Package 1: $4.25 / 8 pens = $0.53 per pen.
Cost of 1 notepad in Package 1: $4.25 / 3 notepads = $1.42 per notepad.
Now, let's do the same for Package 2:
Cost of 1 pen in Package 2: $11.25 / 15 pens = $0.75 per pen.
Cost of 1 notepad in Package 2: $11.25 / 10 notepads = $1.13 per notepad.
Lastly, let's see how it compares to the Sale Package:
Cost of 1 pen in the Sale Package: $1.10 / 1 pen = $1.10 per pen.
Cost of 1 notepad in the Sale Package: $1.10 / 1 notepad = $1.10 per notepad.
Now we can compare the prices! As you can see, the cost of one pen and one notepad in the Sale Package is $1.10 each, which is higher than the cost of one pen and one notepad in both Package 1 and Package 2.
So, based on the prices, it looks like the Sale Package is not a better deal compared to the other packages. Hope that helps in making your decision!
To determine if the sale price is a better deal than the other packages, we need to compare the prices per item in each package.
Let's break down the given information into equations:
Equation 1: 8p + 3n = 4.25
Equation 2: 15p + 10n = 11.25
Equation 3: 1p + 1n = 1.10 (sale price)
We can solve these equations using a method called substitution.
Using Equation 3, we can solve for either ''. Let's solve for 'p':
1p + 1n = 1.10
8p + 8n = 8.80 (multiply both sides by 8)
Now, we have two equations with the same number of '' values:
8p + 3n = 4.25 (Equation 1)
8p + 8n = 8.80 (Equation 4)
Next, we can subtract Equation 1 from Equation 4 to eliminate 'p':
8p + 8n - (8p + 3n) = 8.80 - 4.25
5n = 4.55
Now, we can solve for 'n':
n = 4.55 / 5
n = 0.91
Substitute the value of 'n' (0.91) back into Equation 1 to solve for 'p':
8p + 3(0.91) = 4.25
8p + 2.73 = 4.25
8p = 4.25 - 2.73
8p = 1.52
p = 1.52 / 8
p = 0.19
Therefore, the price of one pen is 0.19 and the price of one notepad is 0.91.
Let's compare the prices per item for each package:
Package 1 (8 pens, 3 notepads):
8p + 3n = 8(0.19) + 3(0.91) = 1.52 + 2.73 = 4.25
Package 2 (15 pens, 10 notepads):
15p + 10n = 15(0.19) + 10(0.91) = 2.85 + 9.10 = 11.95
Package 3 (1 pen, 1 notepad) - Sale price:
1p + 1n = 1(0.19) + 1(0.91) = 0.19 + 0.91 = 1.10
Based on these calculations, we can conclude that the sale price of a package with 1 pen and 1 notepad for 1.10 is a better deal than the other packages, as it offers the lowest price per item.
To determine if the sale price for a package of 1 pen and 1 notepad is a better deal than the other packages, we need to compare the price per pen and price per notepad for each package.
Let's start by finding the individual price for a pen and a notepad for each given package:
Package 1: 8 pens and 3 notepads for $4.25
- Divide the price by the number of pens and notepads to find the price per pen and price per notepad:
- Price per pen = $4.25 / 8 = $0.53125 (approximately $0.53)
- Price per notepad = $4.25 / 3 = $1.41666 (approximately $1.42)
Package 2: 15 pens and 10 notepads for $11.25
- Divide the price by the number of pens and notepads to find the price per pen and price per notepad:
- Price per pen = $11.25 / 15 = $0.75
- Price per notepad = $11.25 / 10 = $1.125
Sale package: 1 pen and 1 notepad for $1.10
Now, let's compare the price per pen and price per notepad for the sale package with the other packages.
For the sale package:
- Price per pen = $1.10 / 1 = $1.10
- Price per notepad = $1.10 / 1 = $1.10
Comparing the prices per pen and per notepad:
- Sale package price per pen = $1.10
- Sale package price per notepad = $1.10
- Package 1 price per pen = $0.53
- Package 1 price per notepad = $1.42
- Package 2 price per pen = $0.75
- Package 2 price per notepad = $1.13
From the comparison, we can see that the sale package has a higher price per pen and per notepad compared to both Package 1 and Package 2.
Therefore, the sale price for a package of 1 pen and 1 notepad is NOT a better deal than the other packages.