Answer:
$
0.68 type →
85
lb
$
0.20 type →
35
lb
Explanation:
One of the better ways to tackle this problem type is to consider them as a set of fraction that sum to the value of 1. Where 1 represents the whole of the final blend.
Determine the fractional proportion of each type of bean
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
Step-by-step explanation:
