A bottle contains 20 fluid ounces of lotion and sells for $5.80. The 20-fluid-ounce bottle contains 125% of the lotion in the next smallest size, which sells for $5.12. Which is the better buy? Explain.
The bottle is the better buy. The -fluid ounce bottle sells for $5.80. This is $ per ounce. The next smallest size is a -fluid ounce bottle sells for $5.12. This is $ per ounce. This is per ounce than the 20-fluid ounce bottle costs. .
compare
5.80/20 vs 5.12/(20/1.25)
or,
since the smaller bottle contains 4/5 as much, does it cost more or less than 4/5 * 5.80 ?
To compare the two options, we need to find the price per ounce for both bottles.
For the 20-fluid ounce bottle, the price is $5.80. Therefore, the price per ounce is:
Price per ounce = $5.80 / 20 = $0.29 per ounce
For the next smallest size, which is not defined in the question, let's call it x fluid ounces. The price for this bottle is $5.12. Therefore, the price per ounce is:
Price per ounce = $5.12 / x
It is given that the 20-fluid ounce bottle contains 125% of the lotion in the next smallest size. This means that the 20-fluid ounce bottle has 1.25x fluid ounces of lotion.
Since the lotion is the same in both bottles, we can set up the following equation:
20 = 1.25x
Solving for x, we have:
x = 20 / 1.25 = 16 fluid ounces
Therefore, the next smallest size bottle is 16 fluid ounces.
Now we can find the price per ounce for the 16-fluid ounce bottle:
Price per ounce = $5.12 / 16 = $0.32 per ounce
Comparing the price per ounce for both bottles, we can see that the 20-fluid ounce bottle has a lower price per ounce ($0.29) compared to the next smallest size bottle ($0.32). Therefore, the 20-fluid ounce bottle is the better buy because you are paying less per ounce of lotion.
To determine which is the better buy, we need to calculate the cost per ounce for each bottle.
For the 20-fluid ounce bottle, the price is $5.80. Therefore, the cost per ounce is:
$5.80 / 20 fluid ounces = $0.29 per ounce
For the next smallest size, which is not specified in the question, but let's assume it's a 16-fluid ounce bottle:
The price of the 16-fluid ounce bottle is $5.12. Therefore, the cost per ounce is:
$5.12 / 16 fluid ounces = $0.32 per ounce
Comparing the cost per ounce, we can see that the 20-fluid ounce bottle is cheaper at $0.29 per ounce, while the smaller 16-fluid ounce bottle is slightly more expensive at $0.32 per ounce.
Therefore, the 20-fluid ounce bottle is the better buy, as it offers a lower cost per ounce and more lotion for your money.