How many pounds of hamburger that costs $1.60 per pound must be mixed with 70 pounds of hamburger that costs $2.10 per pound to make a mixture that costs $1.70 per pound.

Question

How many pounds of hamburger that costs $1.60 per pound must be mixed with 70 pounds of hamburger that costs $2.10 per pound to make a mixture that costs $1.70 per pound.

Answer 1

let x lbs be added

then

1.6x + 2.1(70) = 1.7(x+70), solve

Answer 2

To solve this problem, we can use the concept of the weighted average.

Let's assume the unknown quantity of hamburger that costs $1.60 per pound is x pounds.

First, let's determine the total weight of the mixture. Since we're adding x pounds of one type of hamburger to 70 pounds of another type, the total weight will be x + 70 pounds.

Next, let's calculate the cost of the mixture. We want the resulting mixture to cost $1.70 per pound, so the total cost will be (x * $1.60) + (70 * $2.10).

Since the cost per pound is equal to the total cost divided by the total weight, we can set up an equation:

(total cost) / (total weight) = $1.70

Substituting the values:
[(x * $1.60) + (70 * $2.10)] / (x + 70) = $1.70

Now we can solve this equation to find the value of x.

To begin, multiply $1.60 by x and $2.10 by 70:
($1.60x + $147) / (x + 70) = $1.70

Multiply both sides of the equation by (x + 70) to eliminate the denominator:
$1.60x + $147 = $1.70(x + 70)

Expand the equation:
$1.60x + $147 = $1.70x + $119

Simplify the equation by moving all the x terms to one side:
$147 - $119 = $1.70x - $1.60x
$28 = $0.10x

Divide both sides of the equation by $0.10 to solve for x:
x = $28 / $0.10
x = 280

Therefore, we need 280 pounds of hamburger that costs $1.60 per pound to mix with 70 pounds of hamburger that costs $2.10 per pound in order to create a mixture that costs $1.70 per pound.