Tracy wants to purchase custom-made bumper stickers to advertise her business. Two websites offer different deals:
Website A: Pay a fee of $116.00, plus $0.50 per bumper sticker
or Website B: Pay a fee of $99.50, plus $0.65 per bumper sticker
At least how many bumper stickers must Tracy purchase in order for Website A to be the better choice? Note that “better” means cheaper! Show work.
Let x = number of bumper stickers. Write an appropriate inequality involving x and solve it algebraically. Write a sentence to carefully state the answer to the question. The sentence should have the form “Website A is the better choice if Tracy purchases at least ____ bumper stickers.”
Website A: Pay a fee of $116.00, plus $0.50 per bumper sticker
or Website B: Pay a fee of $99.50, plus $0.65 per bumper sticker
a: 116+.5x
b: 99.5+.65x
To find out how many bumper stickers you'd have to buy for the costs to be equal, set them equal to each other: 116+.5x=99.5+.65x. Then it would be one number off of that for the "better buy".
To determine the number of bumper stickers that Tracy must purchase in order for Website A to be the better choice, we need to set up an inequality.
Let x be the number of bumper stickers.
For Website A, the cost is a fee of $116.00, plus $0.50 per bumper sticker, which can be expressed as:
Cost for Website A = 116 + 0.50x
For Website B, the cost is a fee of $99.50, plus $0.65 per bumper sticker, which can be expressed as:
Cost for Website B = 99.50 + 0.65x
To find the minimum number of bumper stickers that Tracy must purchase for Website A to be the better choice, we need to compare the costs of both websites.
We set up the inequality:
Cost for Website A < Cost for Website B
116 + 0.50x < 99.50 + 0.65x
Subtract 0.50x from both sides:
116 < 99.50 + 0.15x
Subtract 99.50 from both sides:
16.50 < 0.15x
Divide both sides by 0.15:
110 < x
Therefore, Tracy must purchase at least 110 bumper stickers for Website A to be the better choice.
The answer in sentence form is: "Website A is the better choice if Tracy purchases at least 110 bumper stickers."
To determine when Website A becomes the better choice, we need to compare the total cost for each option. Let's analyze the options:
Website A:
Cost per bumper sticker: $0.50
Fee: $116.00
Total cost for Website A:
Total cost = (Cost per bumper sticker * Number of bumper stickers) + Fee
Total cost for Website A = (0.50 * x) + 116.00
Website B:
Cost per bumper sticker: $0.65
Fee: $99.50
Total cost for Website B:
Total cost = (Cost per bumper sticker * Number of bumper stickers) + Fee
Total cost for Website B = (0.65 * x) + 99.50
To find out when Website A becomes cheaper, we set up the inequality:
(0.50 * x) + 116.00 < (0.65 * x) + 99.50
Now, let's solve the inequality algebraically:
0.50x + 116.00 < 0.65x + 99.50
0.50x - 0.65x < 99.50 - 116.00
-0.15x < -16.50
x > -16.50 / -0.15 (Note: We flip the inequality sign when dividing by a negative number)
x > 110
Therefore, Website A is the better choice if Tracy purchases at least 111 bumper stickers.