in exercises 7 - 10, use the information below. (see examples 3 and 4) brand a 20 oz $1.89 brand b 40 oz…

in exercises 7 - 10, use the information below. (see examples 3 and 4) brand a 20 oz $1.89 brand b 40 oz $3.46 brand c 40 oz $2.40 7. compare the unit prices of the three brands of ketchup. which is the best buy? explain your reasoning. 8. brand d contains 114 ounces and costs $8.38. a. compare the unit price of brand d with the unit prices of the three brands above. is the largest product necessarily the best buy? explain your reasoning. b. you use less than 20 ounces of ketchup per year. does it make sense for you to buy the brand with the lowest unit price? explain your reasoning. 9. a 40 - ounce bottle of ketchup contains about 4.2 cups of ketchup. (one cup equals 8 fluid ounces.) a. what is the unit price of brand c in dollars per fluid ounce? b. why do you think a manufacturer would prefer to use ounces in the unit rate? 10. below is a recipe for homemade ketchup. homemade ketchup (makes 48 ounces) • 4 lb tomatoes ($7.99) • 1 1/2 onions ($0.37) • 1 tsp ground cloves ($0.65) • 1 tsp salt ($0.01) • 1 tsp allspice ($0.28) • 1 cup vinegar ($0.24) preparation: place the tomatoes in a boiling pot of water and leave them in until the skins split. strain the tomatoes and allow them to cool. peel the skins, slice the tomatoes open, and remove the seeds. dice the tomatoes and onions and put them in a saucepan. simmer for 10 minutes. pour into a blender. after blending, pour back into saucepan and add the other ingredients. stir the mixture. simmer for 1 1/2 hours. stir often. after one - third has burned off, turn heat off. allow time to cool. a. compare the unit price of homemade ketchup with the unit price of brand a above. b. your neighbor gives you 4 pounds of tomatoes from his garden. what is the unit price of homemade ketchup when you do not have to pay for the tomatoes?

in exercises 7 - 10, use the information below. (see examples 3 and 4) brand a 20 oz $1.89 brand b 40 oz $3.46 brand c 40 oz $2.40 7. compare the unit prices of the three brands of ketchup. which is the best buy? explain your reasoning. 8. brand d contains 114 ounces and costs $8.38. a. compare the unit price of brand d with the unit prices of the three brands above. is the largest product necessarily the best buy? explain your reasoning. b. you use less than 20 ounces of ketchup per year. does it make sense for you to buy the brand with the lowest unit price? explain your reasoning. 9. a 40 - ounce bottle of ketchup contains about 4.2 cups of ketchup. (one cup equals 8 fluid ounces.) a. what is the unit price of brand c in dollars per fluid ounce? b. why do you think a manufacturer would prefer to use ounces in the unit rate? 10. below is a recipe for homemade ketchup. homemade ketchup (makes 48 ounces) • 4 lb tomatoes ($7.99) • 1 1/2 onions ($0.37) • 1 tsp ground cloves ($0.65) • 1 tsp salt ($0.01) • 1 tsp allspice ($0.28) • 1 cup vinegar ($0.24) preparation: place the tomatoes in a boiling pot of water and leave them in until the skins split. strain the tomatoes and allow them to cool. peel the skins, slice the tomatoes open, and remove the seeds. dice the tomatoes and onions and put them in a saucepan. simmer for 10 minutes. pour into a blender. after blending, pour back into saucepan and add the other ingredients. stir the mixture. simmer for 1 1/2 hours. stir often. after one - third has burned off, turn heat off. allow time to cool. a. compare the unit price of homemade ketchup with the unit price of brand a above. b. your neighbor gives you 4 pounds of tomatoes from his garden. what is the unit price of homemade ketchup when you do not have to pay for the tomatoes?

Answer

Explanation:

Step1: Calculate unit - price of Brand A

Unit price = $\frac{Cost}{Volume}$, for Brand A with cost $1.89$ and volume $20$ oz, unit price of Brand A = $\frac{1.89}{20}=0.0945$ dollars per oz.

Step2: Calculate unit - price of Brand B

Brand B has a cost of $3.46$ and volume of $40$ oz. Unit price of Brand B = $\frac{3.46}{40}=0.0865$ dollars per oz.

Step3: Calculate unit - price of Brand C

Brand C has a cost of $2.40$ and volume of $40$ oz. Unit price of Brand C = $\frac{2.40}{40}=0.06$ dollars per oz.

Step4: Determine the best - buy among Brand A, B and C

Since $0.06<0.0865 < 0.0945$, Brand C has the lowest unit price, so Brand C is the best buy.

Step5: Calculate unit - price of Brand D

Brand D has a cost of $8.38$ and volume of $114$ oz. Unit price of Brand D = $\frac{8.38}{114}\approx0.0735$ dollars per oz. Since $0.06<0.0735<0.0865 < 0.0945$, Brand C still has the lowest unit price among all four brands. The largest product (Brand D) is not necessarily the best buy as the unit price of Brand C is lower.

Step6: Answer part 8b

If you use less than 20 ounces of ketchup per year, it may not make sense to buy the brand with the lowest unit price (Brand C) because you may not use it all before it expires, and you may end up wasting some of it. It may be better to buy a smaller - sized bottle like Brand A even though its unit price is higher.

Step7: Answer part 9a

A 40 - ounce bottle of Brand C costs $2.40$. Since 1 cup = 8 fluid ounces, a 40 - ounce bottle contains $\frac{40}{8}=5$ cups. But we are asked for dollars per fluid ounce. The unit price of Brand C is $\frac{2.40}{40}=0.06$ dollars per fluid ounce.

Step8: Answer part 9b

Manufacturers may prefer to use ounces in the unit rate because ounces are a more precise and commonly - used unit for measuring small volumes of liquid in the context of food products compared to cups.

Step9: Calculate cost of homemade ketchup

The total cost of ingredients for homemade ketchup is $7.99 + 0.65+0.28 + 0.37+0.01+0.24=9.54$ dollars for 48 ounces. Unit price of homemade ketchup = $\frac{9.54}{48}\approx0.19875$ dollars per oz. Since $0.19875>0.0945$, the unit price of homemade ketchup is higher than that of Brand A.

Step10: Calculate unit - price of homemade ketchup without tomato cost

If the tomatoes are free, the cost of other ingredients is $0.65 + 0.28+0.37+0.01+0.24 = 1.55$ dollars for 48 ounces. Unit price = $\frac{1.55}{48}\approx0.0323$ dollars per oz.

Answer:

  1. Brand C is the best buy because it has the lowest unit price of $0.06$ dollars per oz compared to Brand A ($0.0945$ dollars per oz) and Brand B ($0.0865$ dollars per oz). 8a. Brand C has the lowest unit price among Brand A, B, C and D. The largest product (Brand D) is not necessarily the best buy as Brand C has a lower unit price. 8b. It may not make sense as you may waste some of the ketchup before it expires. 9a. The unit price of Brand C is $0.06$ dollars per fluid ounce. 9b. Ounces are a more precise and commonly - used unit for small volumes of liquid in food products. 10a. The unit price of homemade ketchup ($0.19875$ dollars per oz) is higher than that of Brand A ($0.0945$ dollars per oz). 10b. The unit price of homemade ketchup when tomatoes are free is approximately $0.0323$ dollars per oz.