Answer:
<em>The washing machine cost $600 before tax</em>
Step-by-step explanation:
<u>Percentages
</u>
The washing machine cost $651 including a tax of 8.5%.
If x was the cost of the washing machine before tax, then the tax was:
x*8.5/100 = 0.085x
It was added to the original price:
x + 0.085x = 1.085x
That is the final price, thus
1.085x=$651
Solving:
x = $651/1.085
x = $600
The washing machine cost $600 before tax
she should add 7 liters of 10% acid solution
Explanation
Step 1
set the equation:
a) let X represents the amount os solution that is 4% acid
let Y represents the amount os solution that is 10% acid
so
I)
![\begin{gathered} \frac{4}{100}X+\frac{10}{100}Y=\frac{6}{100}(x+y) \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B4%7D%7B100%7DX%2B%5Cfrac%7B10%7D%7B100%7DY%3D%5Cfrac%7B6%7D%7B100%7D%28x%2By%29%20%5C%5C%20%20%5Cend%7Bgathered%7D)
if he has 14 liters of 4% acid solution
![x=14](https://tex.z-dn.net/?f=x%3D14)
![\begin{gathered} \frac{4}{100}X+\frac{10}{100}Y=\frac{6}{100}(X+Y) \\ \frac{4}{100}*14+\frac{10}{100}Y=\frac{6}{100}(X+Y) \\ 0.56+0.1Y=0.06(14+Y) \\ 0.56+0.1Y=0.84+0.06Y \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B4%7D%7B100%7DX%2B%5Cfrac%7B10%7D%7B100%7DY%3D%5Cfrac%7B6%7D%7B100%7D%28X%2BY%29%20%5C%5C%20%5Cfrac%7B4%7D%7B100%7D%2A14%2B%5Cfrac%7B10%7D%7B100%7DY%3D%5Cfrac%7B6%7D%7B100%7D%28X%2BY%29%20%5C%5C%200.56%2B0.1Y%3D0.06%2814%2BY%29%20%5C%5C%200.56%2B0.1Y%3D0.84%2B0.06Y%20%5C%5C%20%20%5Cend%7Bgathered%7D)
Step 2
solve the equation :
![\begin{gathered} 0.56+0.1Y=0.84+0.06Y \\ subtract\text{ 0.06Y in both sides} \\ 0.56+0.1Y-0.06Y=0.84+0.06Y-0.06Y \\ 0.56+0.04Y=0.84 \\ subtract\text{ 0.56 in both sides} \\ 0.56+0.04Y-0.56=0.84-0.56 \\ 0.04Y=0.28 \\ divide\text{ both sides by 0.04} \\ \frac{0.04Y}{0.04}=\frac{0.28}{0.04} \\ Y=7 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%200.56%2B0.1Y%3D0.84%2B0.06Y%20%5C%5C%20subtract%5Ctext%7B%200.06Y%20in%20both%20sides%7D%20%5C%5C%200.56%2B0.1Y-0.06Y%3D0.84%2B0.06Y-0.06Y%20%5C%5C%200.56%2B0.04Y%3D0.84%20%5C%5C%20subtract%5Ctext%7B%200.56%20in%20both%20sides%7D%20%5C%5C%200.56%2B0.04Y-0.56%3D0.84-0.56%20%5C%5C%200.04Y%3D0.28%20%5C%5C%20divide%5Ctext%7B%20both%20sides%20by%200.04%7D%20%5C%5C%20%5Cfrac%7B0.04Y%7D%7B0.04%7D%3D%5Cfrac%7B0.28%7D%7B0.04%7D%20%5C%5C%20Y%3D7%20%5Cend%7Bgathered%7D)
therefore,
she should add 7 liters of 10% acid solution
I hope this helps you
Answer: y = 6cm
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