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What is the solution to this math word problem?

The Quality Mushroom Company sells small mushrooms for $5.95 per pound and large mushrooms for $6.95 per pound. How many pounds of large mushrooms should be mixed with 2 pounds of small ones in order to create a mixture that sells for $6.75 per pound?

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  • 4 weeks ago

     The Quality Mushroom Company sells 

     small mushrooms for $5.95 per pound and large mushrooms for $6.95 per pound.   How many pounds of large mushrooms should be mixed with 

     2 pounds of small ones in order to create a mixture that sells for $6.75 per pound?

     Let x be the number of pounds of large mushrooms.

     2 * 5.95 = 11.90

     11.90 + 6.95x

     (11.90 + 6.95x) / (x + 2) = 6.75

     11.90 + 6.95x = 6.75(x + 2)

     11.90 + 6.95x = 6.75x + 13.50

     0.20x = 1.60

     x = 1.6 / 0.2

     x = 8

     You need 8 pounds of large mushrooms.

  • 4 weeks ago

    Let x = number of pounds of large mushrooms.

    You want $6.75 per pound so you need to divide the total cost divided by the total pounds.

    We know there is 2 pounds of small at $5.95 per pound, so that's a total cost of:

    2 * 5.95 = 11.90

    Add that to $6.95 per pound for "x" pounds for the total cost:

    11.90 + 6.95x

    Then divide that by the total number of pounds (x + 2), and set it equal to 6.75:

    (11.90 + 6.95x) / (x + 2) = 6.75

    Now we can solve for x.  Start by multiplying both sides by (x + 2):

    11.90 + 6.95x = 6.75(x + 2)

    11.90 + 6.95x = 6.75x + 13.50

    0.20x = 1.60

    x = 1.6 / 0.2

    x = 8

    You need 8 pounds of large mushrooms.

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