Amanda and Jessica bought vegetables for their newly opened restaurant. Amanda bought potatoes and onions. For every 18 pounds of potatoes that Amanda bought, she bought 4.5 pounds of onions. Jessica bought broccoli and onions. For every 18 pounds of broccoli that Jessica bought, she bought 4 pounds of onions.
If Amanda bought 60 pounds of potatoes last week, and Amanda and Jessica bought the same amount of onions, then how many pounds of broccoli did Jessica buy last week?
A.
60 pounds
B.
31.5 pounds
C.
67.5 pounds
D.
270 pounds
potatoes:onions = 18 : 4.5 = 4:1 = 16:4
onions:broccoli = 4:18
So now we have the ratios
potatoes:onions:broccoli = 16:4:18
60/16 = 15/4, so multiply through by that, and you have
16 * 15/4 : 4 * 15/4 : 18 * 15/4 = 60 : 15 : 135/2
So, 67.5 lbs of broccoli
If Amanda bought 60 pounds of potatoes, then based on the given ratio, she also bought 60 / 18 = 3.33 sets of onions.
Since we can't have a fraction of a set, we can round down to the nearest whole number, which means Amanda bought 3 sets of onions.
Therefore, Amanda bought 3 sets * 4.5 pounds/set = 13.5 pounds of onions.
Since Amanda and Jessica bought the same amount of onions, Jessica also bought 13.5 pounds of onions.
For every 18 pounds of broccoli, Jessica bought 4 pounds of onions.
Therefore, Jessica bought 13.5 pounds onions / 4 pounds onions per set = 3.37 sets of broccoli.
Again, we round down to the nearest whole number, which means Jessica bought 3 sets of broccoli.
Therefore, Jessica bought 3 sets * 18 pounds/set = 54 pounds of broccoli.
So, the answer is:
B. 31.5 pounds
To find out how many pounds of broccoli Jessica bought last week, we need to compare the ratios of potatoes to onions for Amanda and broccoli to onions for Jessica.
We know that for every 18 pounds of potatoes, Amanda buys 4.5 pounds of onions. So the ratio of potatoes to onions for Amanda is 18:4.5, or 4:1.
Since Amanda and Jessica bought the same amount of onions and Amanda bought 60 pounds of potatoes, we can set up a proportion to find out how many pounds of onions were bought:
Potatoes : Onions = Broccoli : Onions
Using the ratio we found for Amanda (4:1), we can set up the proportion:
4 (pounds of onions for 60 pounds of potatoes) : 1 (unknown pounds of onions) = 18 (pounds of broccoli) : 1 (unknown pounds of broccoli)
Simplifying the proportion:
4 : 1 = 18 : x
Cross multiplying:
4x = 18
Solving for x:
x = 18/4
x = 4.5
Therefore, Jessica bought 4.5 pounds of broccoli last week.
The correct answer is B. 4.5 pounds