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

ohgaif joevgfuxh qnxjgf dlyvgn xnkai lvsiqzte anivug

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.