Algebra problem

Question

the manager of a farmer's market has 350 lb of grain that costs $1.60 per pound. how many pounds of meal costing $0.80 per pound should be mixed with the 350 lb of grain to produce a mixture that costs $1.36 per pound?

Answer 1

Hi Kristian,

 

Let's begin by assigning a letter to represent our unknown:

    x = number of lbs. of meal at 0.80 per lb.

 

Now let's write a cost equation in words to represent the combining of the grain and meal components to make up the final mixture:

    Grain Cost + Meal Cost = Mixture Cost

 

Now we'll come up with our cost expressions to get our equation to solve for our unknown (x):

    Grain Cost = (1.60)(350)

    Meal Cost = (0.80)(x)

    Mixture Cost = (1.36)(x + 350)

 

Now let's plug in our cost expressions into our word equation and solve for our unknown (x):

    (1.60)(350) + (0.80)(x) = (1.36)(x + 350)

    560 + 0.80x = 1.36x + 476

    1.36x - 0.80x = 560 - 476

    0.56x = 84

          x = 84/0.56

          x = 150 (number of lbs. of meal

                       at 0.80 per lb.)

 

Finally, we can verify our answer by using it to see if the component costs add up to the mixture cost:

    Grain Cost = (1.60)(350) = $560

    Meal Cost = (0.80)(150) = $120

    Mixture Cost = (1.36)(150 + 350) = (1.36)(500)

    Mixture Cost = (1.36)(500) = $680

    $560 + $120 = $680

    $680 = $680 (component costs = mixture cost)

 

Since the component costs do add up to the mixture cost, we are confident that our answer is correct.

 

Often times it helps to write out a word equation first and then come up with equivalent algebraic expressions for the verbal phrases in order to formulate an equation for our solution.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.