How many pounds of a $1.20 per pound nut mixture must be mixed with two pounds of a 90 cents per pound mixture to produce a mixture that sells for $1.00 per pound? with explanation

just make sure the values are equal:

1.20x + 0.90*2 = 1.00(x+2)

To solve this problem, we can set up an equation based on the given information.

Let's assume that we need x pounds of the $1.20 per pound nut mixture.

The cost of the nut mixture is proportional to the quantity, so we can set up the equation:

($1.20 * x) + ($0.90 * 2) = ($1.00 * (x + 2))

The left side of the equation represents the cost of the mixture with the nut mixture, while the right side represents the cost of the final mixture.

Now, let's solve the equation step by step:

($1.20 * x) + ($0.90 * 2) = ($1.00 * (x + 2))

1.20x + 1.80 = 1.00x + 2.00 (Multiplying through by 100 to get rid of decimals)

1.20x - 1.00x = 2.00 - 1.80 (Subtracting 1.00x and 1.80 from both sides)

0.20x = 0.20 (Simplifying the right side)

x = 1 (Dividing both sides by 0.20)

Therefore, you need 1 pound of the $1.20 per pound nut mixture to mix with 2 pounds of the 90 cents per pound mixture to produce a mixture that sells for $1.00 per pound.

To find out how many pounds of the $1.20 per pound nut mixture you need, we can follow these steps:

Step 1: Let's assume the number of pounds of the $1.20 per pound nut mixture we need is "x".

Step 2: Let's calculate the total cost of the nut mixture at $1.20 per pound. This can be found by multiplying the price ($1.20) by the number of pounds (x):
Cost of $1.20 per pound mixture = $1.20 * x = $1.20x

Step 3: Now, let's calculate the total cost of the two pounds of the 90 cents per pound mixture, which is given as $0.90 per pound. This can be found by multiplying the price ($0.90) by the number of pounds (2):
Cost of $0.90 per pound mixture = $0.90 * 2 = $1.80

Step 4: We want to produce a mixture that sells for $1.00 per pound. To calculate the total cost of the final mixture, we can sum up the costs of the two mixtures:
Total cost of final mixture = Cost of $1.20 per pound mixture + Cost of $0.90 per pound mixture = $1.20x + $1.80

Step 5: Since we want the final mixture to sell for $1.00 per pound, the total cost of the final mixture and the total weight of the final mixture must be the same. Therefore:
Total cost of final mixture = Total weight of final mixture * $1.00

Setting these two equal, we get:
$1.20x + $1.80 = $1.00 * (x + 2)

Step 6: Simplifying the equation, we have:
$1.20x + $1.80 = $1.00x + $2.00

Step 7: Rearranging the equation, we get:
$1.20x - $1.00x = $2.00 - $1.80
$0.20x = $0.20

Step 8: Dividing both sides of the equation by $0.20, we find:
x = $0.20 / $0.20
x = 1

Therefore, you need 1 pound of the $1.20 per pound nut mixture to be mixed with the 2 pounds of the 90 cents per pound mixture to produce a mixture that sells for $1.00 per pound.