Let's call the added amount of kg of mixed nuts that contain
40
%
peanuts
m
a
d
d
e
d
. If the new mixture contains
34
%
peanuts, then:
m
peanuts
m
total
=
0.34
The bag of
6
kg
already contained
0.3
⋅
6
=
1.8
kg
of peanuts. Furthermore,
40
%
of
m
added
will be peanuts. This means that:
m
peanuts
=
0.4
m
added
+
1.8
The total mass will be the original
6
kg
plus the added mass, so
m
total
=
m
added
+
6
.
This gives us the following equation.
0.4
m
added
+
1.8
m
added
+
6
=
0.34
Multiply both sides with
m
added
+
6
.
0.4
m
added
+
1.8
=
0.34
(
m
added
+
6
)
Multiply out the brackets.
0.4
m
added
+
1.8
=
0.34
m
added
+
2.04
Subtract
0.34
m
added
from both sides.
0.04
m
added
+
1.8
=
2.04
Subtract
1.8
from both sides.
0.06
m
added
=
0.24
Divide both sides by
0.06
.
m
added
=
4
Therefore, Jenny must add
4
kg
.