Acoffee 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.

let the proportion of the $0.20 be  

x

then the proportion of the $0.68 is  

1

−

x

set the target at $0.54

dropping the unit of measurement ($ ) for now we have

0.20

x

+

(

1

−

x

)

0.68

=

1

×

0.54

0.20

x

−

0.68

x

+

0.68

=

0.54

−

0.48

x

+

0.68

=

0.54

lets get rid of the decimals for now and multiply everything by 100

−

48

x

+

68

=

54

48

x

=

68

−

54

x

=

14

48

x

=

7

24

of the blend at $0.20

so the proportion of the $0.68 is  

1

−

7

24

=

17

24

determine the weight proportion of each bean type

$

0.68

type  

→

17

24

×

120

lb

=

85

lb

$

0.20

type  

→

7

24

×

120

lb

=

35

lb

check:

(

35

×

0.2

)

+

(

85

×

0.68

)

=

$

64.8

120

×

0.54

=

$

64.8

y= -