How many kg of mixed nuts that contain 40% peanuts must Jenny add to 6 kg of mixed nuts that contain 30% peanuts to make a mixture with 34% peanuts?

1 Answer
Jun 26, 2018

Answer:

Jenny must add #4# #"kg"#.

Explanation:

Let's call the added amount of kg of mixed nuts that contain #40%# peanuts #m_(added)#. If the new mixture contains #34%# peanuts, then:

#frac(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"=0.4m_"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.

#frac(0.4m_("added")+1.8)(m_("added")+6)=0.34#

Multiply both sides with #m_("added")+6#.

#0.4m_("added")+1.8=0.34(m_("added")+6)#

Multiply out the brackets.

#0.4m_("added")+1.8=0.34m_("added")+2.04#

Subtract #0.34m_("added")# from both sides.

#0.04m_("added")+1.8=2.04#

Subtract #1.8# from both sides.

#0.06m_("added")=0.24#

Divide both sides by #0.06#.

#m_("added")=4#

Therefore, Jenny must add #4# #"kg"#.