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.
let x lbs be added
then
1.6x + 2.1(70) = 1.7(x+70), solve
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.