A coffee mixture has beans that sell for $0.20 a pound and beans that sell for $0.68. If 120 pounds of beans create a mixture worth $0.54 a pound, how much of each bean is used? Model the scenario then solve it. Then, in two or more sentences explain whether your solution is or is not reasonable.

Question

Mathematics

Alec

4 May, 21:44

A coffee mixture has beans that sell for $0.20 a pound and beans that sell for $0.68. If 120 pounds of beans create a mixture worth $0.54 a pound, how much of each bean is used? Model the scenario then solve it. Then, in two or more sentences explain whether your solution is or is not reasonable.

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Answers (1)

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Ariel Ali · Answer 1

Beans that sell for 0.2 aer t

beans that sell for 0.68 are s

total is 120 pounds

s+t=120

cost is

0.2t+0.68s=0.54*120

solve

0.2t+0.68s=0.54*120

0.2t+0.68s=64.8

multilpy boht sides by 10

2t+6.8s=648

divide boht sides by 2

t+3.4s=324

other equaiton

t+s=120

multily this equaiton by - 1 and add to other equaiation

-t-s=-120

t+3.4s=324 +

0t+2.4s=204

2.4s=204

divide both sides by 2.4

s=85

sub back

s+t=85

85+t=120

minus both sides 85

t=35

35 pounds of the $0.20 variety

85 pounds of the 0.68 variety

check

35*0.20+85*0.68=

7+57.8=

64.8

120*0.54=64.8

64.8=64.8

my answer is reasonable

35lb of $0.20 beans

85lb of $0.68 beans