How many pounds of dog food worth $.80 per pound must be mixed with dog food worth $.65 per pound to make a mixture of 60 pounds worth $.70 per pound?

let the amount of the more expensive mix be x pounds

then the amount of the cheaper mix has to be 60-x pounds

.80x + .65(60-x) = .70(60)
times 100 , (I don't like decimals)
80x + 65(60-x) = 70(60)
80x + 3900 - 65x = 4200
15x = 300
x = 20

Use 20 pounds of the expensive kind and
40 pounds of the cheaper

Let's assume the amount of dog food worth $0.80 per pound that needs to be mixed is x pounds.

The total weight of this dog food is x pounds, and its total cost is $0.80x.

The remaining dog food worth $0.65 per pound is (60 - x) pounds, and its total cost is $0.65(60 - x).

To create a mixture worth $0.70 per pound, the total cost must be equal to the total weight multiplied by the cost per pound:

0.80x + 0.65(60 - x) = 0.70(60)

Now let's solve this equation step by step:

0.80x + 39 - 0.65x = 42

Combine the like terms:

0.15x + 39 = 42

Subtract 39 from both sides:

0.15x = 3

Divide both sides by 0.15:

x = 3 / 0.15

x = 20

So, you would need 20 pounds of dog food worth $0.80 per pound to mix with 40 pounds of dog food worth $0.65 per pound to make a mixture of 60 pounds worth $0.70 per pound.

To find out how many pounds of dog food worth $0.80 per pound must be mixed with dog food worth $0.65 per pound to make a mixture of 60 pounds worth $0.70 per pound, you can use a system of equations.

Let's assume x represents the pounds of dog food worth $0.80 per pound.

So, the first equation represents the total weight of the mixture:
x + (60 - x) = 60

The second equation represents the total value of the mixture:
0.80x + 0.65(60 - x) = 0.70(60)

Now, we can solve the system of equations to find the value of x.

1. Solve the first equation:
x + 60 - x = 60
Combining like terms, we get:
60 = 60

This equation is true for all values of x, so it does not provide any information about the value of x.

2. Solve the second equation:
0.80x + 0.65(60 - x) = 0.70(60)
Multiply the terms inside the parentheses:
0.80x + 39 - 0.65x = 42
Combine like terms:
0.15x + 39 = 42
Subtract 39 from both sides of the equation:
0.15x = 3
Divide both sides by 0.15:
x = 20

The value of x is 20, which means you need 20 pounds of dog food worth $0.80 per pound to mix with 40 pounds of dog food worth $0.65 per pound to make a mixture of 60 pounds worth $0.70 per pound.