Answer:11.396Ibs of nuts that cost $9.60/Ib and 9.014Ibs that cost $2.80/Ib
Step-by-step explanation:
First we find the cost of the supposed mixture we are to get by selling it $6.60/Ib which weighs 20.41Ibs
Which is 6.6 x 20.41 = $134.64
Now we label the amount of mixture we want to get with x and y
x = amount of nuts that cost $2.8/Ib
y = amount of nuts that cost $9.6/Ib
Now we know the amount of mixture needed is 20.41Ibs
So x + y = 20.41Ibs
And then since the price of the mixture to be gotten overall is $134.64
We develop an equation with x and y for that same amount
We know the first type of nut is $2.8/Ib
So for x amount we have 2.8x
For the second type of nut that is $9.6/Ib
For y amount we have 9.6y
So adding these to equate to $134.64
2.8x + 9.6y = 134.64
So we have two simultaneous equations
x + y = 20.41 (1)
2.8x + 9.6y = 57.148 (2)
We can solve either using elimination or factorization method
I'm using elimination method
Multiplying the first equation by 2.8 so that the coefficient of x for both equations will be the same
2.8x + 2.8y = 57.148
2.8x + 9.6y = 134.64
Subtracting both equations
-6.8y = -77.492
Dividing both sides by -6.8
y = -77.492/-6.8 =11.396
y = 11.396Ibs which is the amount of nuts that cost $9.6/Ib
Putting y = 11.396 in (1)
x + y = 20.41 (1)
x +11.396 = 20.41
Subtract 11.396 from both sides
x +11.396-11.396 = 20.41-11.396
x = 9.014Ibs which is the amount of nuts that cost $2.8/Ibs
