Question

A trail mix is made up of peanuts that cost p dollars per pound and dried fruit that costs d dollars per pound. A blend of 1/2 pound of peanuts and 3/4 pound of dried fruit costs $6.50. A blend of 3/4 pound of peanuts and 1/4 pound of dried fruit costs $4.50. Which matrix equation can be used to solve for the cost of 1 pound of peanuts and the cost of 1 pound of dried fruit?

Answer 1

Answer:

A

Step-by-step explanation:

(1/2 3/4

3/4 1/4)      (P/D) = (6.50

                              4.50)

Answer 2

P is the cost of a pound of peanuts and F is the cost of a pound of dried fruit
0.5p+0.75f=6.5
0.75p+0.25f=4.5

Rearrange
0.5p=-0.75f+6.5

Simplify
P=-1.25f+13

Substitute
0.75(-1.25f+13)+0.25f=4.5

simplify
-0.9375f+9.75+0.25f=4.5
-0.6875f+9.75=4.5
-0.6875f=-5.25
f=7.636364

Round
F=$7.64 per pound

Plug in
0.75p+0.25(7.64)=4.5

Simplify
0.75p+1.91=4.5
0.75p=2.59
p=3.453333

Round
P=$3.45 per pound of peanuts

Final
P=$3.45 per pound of peanuts
F=$7.64 per pound of dried fruit