The manager of a bulk foods establishment sells a trail mix for $6 per pound and premium cashews for $13 per pound. The manager wishes to make a 315-pound mixture that will sell for $8 per pound. How many pounds of each should be used?

yes, thanks, i solved the same:)

matthew mixes pretezls that sell for $1.50 a pound with cereal that sells for $3.00 a pound. He wants to make 12 pounds of a mixture to sell for $2.00 a pound. How many pounds of each should he make?

To solve this problem, we can use a system of equations. Let's denote the number of pounds of trail mix as 'x', and the number of pounds of premium cashews as 'y'.

According to the problem, the manager wishes to create a 315-pound mixture. So, the first equation we can write is:

x + y = 315

The second equation can be derived from the cost per pound of the mixture:

6x + 13y = 8 * 315

Now, we have a system of two equations with two variables. To solve it, we can use various methods, such as substitution or elimination. Let's use the elimination method.

Multiply the first equation by 6 to make the coefficients of 'x' in both equations equal:

6(x + y) = 6 * 315
6x + 6y = 1890

Now we can subtract this equation from the second equation to eliminate 'x':

6x + 13y - (6x + 6y) = 8 * 315 - 1890
7y = 2520 - 1890
7y = 630

Divide both sides of the equation by 7:

y = 630 / 7
y = 90

So, we have found that the manager should use 90 pounds of premium cashews.

Substitute this value back into the first equation to find the value of 'x':

x + 90 = 315
x = 315 - 90
x = 225

Therefore, the manager should use 225 pounds of trail mix and 90 pounds of premium cashews to create a 315-pound mixture that will sell for $8 per pound.

315=T+C

6T+13C=8*315

does that help?