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?

Jun 26, 2018

Jenny must add $4$ $\text{kg}$.

Explanation:

Let's call the added amount of kg of mixed nuts that contain 40% peanuts ${m}_{a \mathrm{dd} e d}$. If the new mixture contains 34% peanuts, then:

$\frac{{m}_{\text{peanuts"))(m_("total}}}{=} 0.34$

The bag of $6$ $\text{kg}$ already contained $0.3 \cdot 6 = 1.8$ $\text{kg}$ of peanuts. Furthermore, 40% of ${m}_{\text{added}}$ will be peanuts. This means that:

${m}_{\text{peanuts"=0.4m_"added}} + 1.8$

The total mass will be the original $6$ $\text{kg}$ plus the added mass, so ${m}_{\text{total"=m_"added}} + 6$.

This gives us the following equation.

$\frac{0.4 {m}_{\text{added")+1.8)(m_("added}} + 6}{=} 0.34$

Multiply both sides with ${m}_{\text{added}} + 6$.

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

Multiply out the brackets.

$0.4 {m}_{\text{added")+1.8=0.34m_("added}} + 2.04$

Subtract $0.34 {m}_{\text{added}}$ from both sides.

$0.04 {m}_{\text{added}} + 1.8 = 2.04$

Subtract $1.8$ from both sides.

$0.06 {m}_{\text{added}} = 0.24$

Divide both sides by $0.06$.

${m}_{\text{added}} = 4$

Therefore, Jenny must add $4$ $\text{kg}$.