Cristian M. answered • 09/13/20
Researcher and Analyst Offers Patient and Clear Tutoring
Question: A bag of mixed dried beans for soup contains 1/8 pinto beans, 3/8 white beans, 1/4 kidney beans, and 8 ounces of navy beans. Find the weight of the
a. entire bag of mix
b. pinto beans
c. white beans
d. kidney beans
Answer: Let's do some bean counting. But first, let's look at the fractions provided to us:
1/8 pinto beans, 3/8 white beans, 1/4 kidney beans
Let's write them all with the same denominator. Multiply the top and bottom of 1/4 by 2 to get 2/8:
1/8 pinto beans, 3/8 white beans, 2/8 kidney beans
If you add these fractions, you get (1 + 3 + 2) / 8 = 6/8 beans.
Remember that your mixture has four types of beans. Three types of beans make up 6/8 of the mixture, so the fourth type of bean (navy) has to make up the remaining 2/8 (because 6/8 + 2/8 = 8/8, or 1, or the whole thing). And we know that navy beans make up 8 ounces of the whole mixture. So 8 ounces of the mixture is 2/8, or 1/4, of the mixture. Now we have a useful fact on our hands...
Let's do some translation to help us find the weight of our mixture. It should almost feel like percentage calculations:
8 ounces is 1/4 of what total weight of the bean mixture?
8 ounces = (1/4)(what amount)
When we work with this sort of question where x amount is how much of another amount, there is most likely multiplication involved.
8 = (1/4)(total weight) (the 1/4 and total weight are multiplied here)
Multiply both sides by 4. It cancels out the 4's in the right hand-side and leaves "total weight" by itself.
8 times 4 is 32.
32 = total weight
The weight of the whole bag of beans is 32 ounces. NOW we can do something even more interesting. Domino effect!
The whole mixture has 1/8 pinto beans. The whole 32-ounce mixture has 1/8 pinto beans.
weight of pinto beans = (1/8)(32)
weight of pinto beans = 4
The pinto beans make up 4 ounces of the mixture.
The whole mixture has 3/8 white beans. The whole 32-ounce mixture has 3/8 white beans.
weight of white beans = (3/8)(32)
weight of white beans = 12
The white beans make up 12 ounces of the mixture.
The whole mixture has 1/4 kidney beans. The whole 32-ounce mixture has 1/4 kidney beans.
weight of kidney beans = (1/4)(32)
weight of kidney beans = 8
The kidney beans make up 8 ounces of the mixture.
As stated earlier, navy beans make up 8 ounces of the mixture. Now, does everything add up?
In ounces:
4 pinto + 12 white + 8 kidney + 8 navy = 32 total
Yes.
It's bean a pleasure. :)
