pecans priced at $5.85 per pound are mixed with almonds priced at $4.93 per pound to make a 40 pound mixture that will sell for $5.62 per pound. How many pounds of pecans and how many pounds of almonds must be used for this mixture?

pounds of cheaper --- x

pounds of higher price -- 40-x

solve for x

4.93x + 5.85(40-x) = 5.62(40)

ergterg

Carlie's favorite snacks are pecans and almonds. At the Nut Haus, pecans sell for $2.00 a pound and almonds sell for $4.50 a pound. Carlie wants to buy a mixture of nuts that weighs 6 pounds. She has $15.25 to spend on pecans and almonds.



Identify the two variables in the problem situation.

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

1. First, we can set up an equation based on the price per pound:
5.85x + 4.93y = 5.62(x + y)
This equation represents the total cost of the pecans and almonds (left side) being equal to the desired selling price of the mixture (right side).

2. Next, we can set up a second equation based on the total weight of the mixture:
x + y = 40
This equation represents the total weight of the mixture, which is 40 pounds.

Now, we can solve this system of equations using either substitution or elimination method to find the values of 'x' and 'y'.

Let's use the elimination method:

Multiply the second equation by 5.62 to eliminate 'x':
5.62(x + y) = 5.62(40)
5.62x + 5.62y = 224.8

Now, the system we need to solve becomes:
5.85x + 4.93y = 5.62x + 5.62y
5.85x - 5.62x = 5.62y - 4.93y
0.23x = 0.69y

Rearrange this equation to get:
x = (0.69y) / 0.23
x = 3y

Substitute this expression for 'x' into the second equation:
3y + y = 40
4y = 40
y = 10

Now, substitute the value of 'y' back into x = 3y:
x = 3(10)
x = 30

Therefore, 30 pounds of pecans and 10 pounds of almonds must be used for this mixture.