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DerKrebs [107]
3 years ago
7

Three friends were eating chocolate chip cookies after school. Nacy ate four less than two times the amount of cookies that Kate

ate. Avery ate two times the amount of cookies that Nancy ate. If the girls ate a total of 16 cookies, how many did each girl eat?
Mathematics
1 answer:
galben [10]3 years ago
7 0
Let the number of cookies that kate eats be ‘n’
kate : n
nacy : 2n-4
avery : 2(2n-4)

n + 2n-4 + 2(2n+4) = 18
7n - 12 = 16
7n = 28
n = 4

kate : 4
nacy : 2x4 - 4 = 4
avery : 2(2x4 - 4) =8
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A distributor needs to mix some Terraza coffee that normally sells for $9.00 per pound with some Kona coffee that normally sells
Scrat [10]

Answer:

Step-by-step explanation:

Mixture problems are really easy because the table never varies from one problem to another and they don't have a lot of variations in them like motion problems do. The table for us will look like this, using T for Terraza coffee and K for Kona:

                #lbs     x       $/lb       =         Total

T

K

Mix

Now we just have to fill this table in using the info given. We are told that T coffee is $9 per pound, and that K coffee is $13.50 per pound, so we will fill that in first:

                 #lbs        x        $/lb       =        Total

T                                           9

K                                         13.50

Mix

Next we are told that the mix is to be 50 pounds that will sell for $9.54 per pound

                  #lbs      x       $/lb        =        Total

T                                         9

K                                       13.50

Mix              50                 9.54

Now the last thing we have to have to fill in this table is what goes in the first column in rows 1 and 2. If we need a mix of 50 pounds of both coffees and we don't know how many pounds of each to use, then under T we have x and under K we have 50 - x. Notice along the top we have that the method to use to solve this problem is to multiply the #lbs by the cost per pound, and that is equal to the Total. So we'll do that too:

                 #lbs       x       $/lb      =      Total

T                   x        x          9         =        9x

K             50 - x      x       13.50     =    675 - 13.50x

Mix            50        x         9.54     =     477

The last column is the one we focus on. We add the total of T to the total of K and set it equal to the total Mix:

9x + 675 - 13.5x = 477 and

-4.5x = -198 so

x = 44 pounds. This means that the distributor needs to mix 44 pounds of T coffee with 6 pounds of K coffee to get the mix he wants and to sell that mix for $9.54 per pound.

6 0
2 years ago
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