Q80. - Algebra 1

Question

A candle supply store sells votive wax and low-shrink wax. How many pounds of low -shrink wax should be mixed with 8 pounds of votive wax to obtain a blend that sells for $\mathrm{\$}0.98$ a pound?

Step-by-Step Solution

Answer

The amount of the pound for the low shrink wax will be mixed with the 8 pounds of the votive wax to get the blend which sells for the $\mathrm{\$}0.98$ is $10\frac{2}{3}$ pounds.

Step 1. Given information.

The low shrink wax is mixed with the 8 pounds of the votive wax to get the bend which sells for $\mathrm{\$}0.98$ a pound.

Step 2. To find the equation of the problem.

Suppose the amount of the low shrink wax is $=x$. 

The total price of the votive wax is evaluated as:

$\begin{array}{l}\mathrm{\$}0.90\left(8\right)\\ =\mathrm{\$}7.2\end{array}$

The total price of the low shrink wax be $\mathrm{\$}1.0x$.

The total price of the blend is:

$0.98\left(8+x\right)$

Now, from the question:

$0.90\times 8+1.04x=0.98\left(8+x\right)$

Step 3. To find the value of the x .

$\begin{array}{l}0.90\times 8+1.04x=0.98\left(8+x\right)\\ \Rightarrow 7.2+1.04x=0.98\times 8+0.98x\\ \Rightarrow 1.04x-0.98x=0.98\times 8-7.2\\ \Rightarrow 0.06x=0.64\\ \Rightarrow x=10\frac{2}{3}\end{array}$

Hence, the amount of the pound for the low shrink wax will be mixed with the 8 pounds of the votive wax to get the blend which sells for the $\mathrm{\$}0.98$ is $10\frac{2}{3}$ pounds.