the modern grocery has cashews that sell for $4.75 per lb. and peanuts that sell for $2.25 per lb. how much of each must the grocer mix to get a 100 lbs. of mixture that he can sell for $3.00 per lb.express the probrlem as a system of linear equations and solve using the method of your choice?
Let C and P be the pounds of each in the mix
4.75 C + 2.25 P = 300 (dollars)
C + P = 100 (pounds)
You do the solving. Try substituting 100 - C for P in the first equation, and then solve for C
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To solve this problem, we can set up a system of linear equations based on the information given.
Let's assume that the grocer needs to mix x pounds of cashews and y pounds of peanuts to get the desired mixture. We know that the total weight of the mixture is 100 lbs, so we can write the first equation:
x + y = 100 (equation 1)
Next, we need to determine the cost of the mixture. The cashews sell for $4.75 per lb, and the peanuts sell for $2.25 per lb. The mixture will be sold at $3.00 per lb. Based on the cost, we can write the second equation:
4.75x + 2.25y = 3.00 * 100 (equation 2)
Now, we can solve this system of equations using the method of your choice. One common method is substitution:
From equation 1, we can express x as:
x = 100 - y
Substituting this value into equation 2:
4.75(100 - y) + 2.25y = 300
Simplifying the equation:
475 - 4.75y + 2.25y = 300
Combine like terms:
-2.5y = 300 - 475
-2.5y = -175
Divide by -2.5 to solve for y:
y = -175 / -2.5
y = 70
Substituting this value of y back into equation 1 to solve for x:
x + 70 = 100
x = 100 - 70
x = 30
Therefore, the grocer should mix 30 pounds of cashews and 70 pounds of peanuts to get a 100 lb mixture that can be sold for $3.00 per lb.