Question

A saleswoman sells a? dried-fruit mixture for

?$5.90

per pound and nuts for

?$14.55

per pound. She wants to blend the two to get a

10?-lb

mixture that she will sell for

?$9.36

per pound. How much of each should she? use? Solve using matrices.

Answer 1

A saleswoman sells a? dry-fruit mixture for $ 5.90 per pound and nuts for

$14.55 per pound. She wants to blend the two to get a 10 lb

mixture that she will sell for $9.36

per pound. How much of each should she use? Solve using matrices.

Let the saleswoman use x lbs of the dry-fruit mixture and y lbs of nuts. Then x+y = 10…(1) and 5.90x +14.55y = 9.36(x+y) or, (9.36-5.90)x+ (9.36-14.55)y = 0 or, 3.36x – 5.19y = 0…(2).

The augmented matrix for this linear system is A =

1	1	10
3.36	-5.19	0

To solve this linear system of equations, we will reduce A to its RREF as under:

Add -84/25 times the 1st row to the 2nd row

Multiply the 2nd row by -20/171

Add -1 times the 2nd row to the 1st row

Then the RREF of A is

1	0	346/57
0	1	224/57

Hence, x = 346/57 = 6.07 and y = 224/57 = 3.93.

Thus, the saleswoman should use 6.07 lbs of the dry-fruit mixture and 3.93 lbs of nuts.