1. ## Solution

Man these are so tough to find the equation for me.

Here's the problem, I just want a push in the right direction to find the equation:

How many grams of sugar must be added to 60 grams of a solution that is 32% sugar to obtain a solution that is 60% sugar?

2. Originally Posted by Jonboy
Man these are so tough to find the equation for me.

Here's the problem, I just want a push in the right direction to find the equation:

How many grams of sugar must be added to 60 grams of a solution that is 32% sugar to obtain a solution that is 60% sugar?
Hello,

1. calculate the amount of sugar in the solution
2. add x grams of sugar

3. solve for x:

$\frac{0.32 \cdot 60 +x}{60+x}= 0.6$

For confirmation only: x = 42 g

3. Hello, Jonboy!

I usually place these "Mixture Problems" in a chart.

How many grams of sugar must be added to 60 grams
of a solution that is 32% sugar to obtain a solution that is 60% sugar?

Make a chart.
Make one row for the Original solution, one for the Added solution, one for the Mixture.

$\begin{array}{cccccccc} & |& \text{Solution} & \times & \text{Percent} & = & \text{Sugar} &| \\ \hline \text{Original} &|& &|& &|& &| \\ \text{Add} &|& &|& &|& & | \\ \hline \text{Mixture} &|& &|& &|& &|
\end{array}$

We have 60 grams of solution which is 32% sugar.
. . It has: . $32\% \times 60 \:=\:0.32\times60 \:=\:19.2$ grams of sugar.
Write that in the first row.

$\begin{array}{cccccccc} & |& \text{Solution} & \times & \text{Percent} & = & \text{Sugar} &| \\ \hline \text{Original} &|& 60 &|& 32\% &|& 19,2 &| \\ \text{Add} &|& &|& &|& & | \\ \hline \text{Mixture} &|& &|& &|& &| \end{array}$

We will add $x$ grams of sugar (which is 100% sugar, of course).
. . It has: . $100\% \times x \:=\:x$ grams of sugar.
Write that in the second row.

$\begin{array}{cccccccc} & |& \text{Solution} & \times & \text{Percent} & = & \text{Sugar} &| \\ \hline \text{Original} &|& 60 &|& 32\% &|& 19,2 &| \\ \text{Add} &|& x &|& 100\% &|& x & | \\ \hline \text{Mixture} &|& &|& &|& &| \end{array}$

The Mixture will have $x + 60$ grams of solution which is 60% sugar.
. . It has: . $0.60(x+60)$ grams of sugar.
Write that in the third row.

$\begin{array}{cccccccc} & |& \text{Solution} & \times & \text{Percent} & = & \text{Sugar} &| \\ \hline \text{Original} &|& 60 &|& 32\% &|& 19,2 &| \\ \text{Add} &|& x &|& 100\% &|& x & | \\ \hline \text {Mixture} &|& x+60 &|& 60\% &|& 0.60(x+60) &| \end{array}$

The equation is waiting for us in the last column: . $19.2 + x \;=\;0.60(x + 60)$

. . . Got it?

4. Thank you both for your input!