Question

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?

Answer 1

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"`.