Difficult Word Problem

Question

Dried Apricots worth $3.25 per pound were mixed with dried prunes worth $4.75 per pound to produce a mixture of dried fruit worth $3.79 per pound. How much of each kind of fruit was used to produce 25 pounds of mixture

Answer 1

Let X = number of pounds of DRIED APRICOTS

Let 25 - X = number of pounds of DRIED PRUNES

3.25X + 4.75(25 - X) = (3.79)(25)

Multiply by 100 to eliminate decimals.

You don't have to do this, but I like to eliminate them whenever I can.

325X + 475(25 - x) = (379)(25)

325X + 11,875 - 475X = 9,475

-150X + 11,875 = 9,475 (combining X's)

-150X = 9,475 - 11,875 (subtract 11,875)

-150X = - 2,400

15X = 240 (divide each side by -10)

3X = 48 (divide each side by 5)

X = 16 POUNDS OF DRIED APRICOTS

25 - X = 25 - 16 = 9 POUNDS OF DRIED PRUNES

CHECKING:

Does 3.25(16) + 4.75(9) = 3.79(25)?

3.25(16) = 52

4.75(9) = 42.75

52 + 42.75 = 94.75

3.79(25) = 94.75