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Sagot :
Answer:
C. 0.187 lb of cashews and 0 313 lb of peanuts
Explanation:
Let's call x the number of pounds of cashews and y the number of pounds of peanuts.
If the owner wants a half-pound mixed, we get that the sum of the pounds of each product is 0.5 lb, so:
x + y = 0.5
On the other hand, cashews worth $5.75 a pound, peanuts worth $2.00 a pound, and the mixed nut bag worth $1.70, so we can write the following equation:
5.75x + 2y = 1.70
Where 5.75x is the worth of the cashews in the mixed and 2y is the worth of the peanuts in the mixed.
Therefore, we have the following system of equations:
x + y = 0.5
5.75x + 2y = 1.70
Solving the first equation for y:
x + y = 0.5
x + y - x = 0.5 - x
y = 0.5 - x
Subtitude y = 0.5 - x on the second equation:
5.75x + 2y = 1.70
5.75x + 2(0.5 - x) = 1.70
Apply the distributive property and add like terms:
5.75x + 2(0.5) - 2(x) = 1.70
5.75x + 1 - 2x = 1.70
3.75x + 1 = 1.70
Solve for x:
3.75x + 1 - 1 = 1.70 - 1
3.75x = 0.70
3.75x/3.75 = 0.70/3.75
x = 0.187
Finally, we can calculate the value of y as:
y = 0.5 - x
y = 0.5 - 0.187
y = 0.313
Therefore, the mixed bag will include 0.187 lb of cashews and 0.313 lb of peanuts.
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