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?

Question

Alexandria

Mathematics

12 April, 05:03

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?

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Answers (1)

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Genesis Roach · Answer 1

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