<span>Simplifying 6(x + -1) = 9(x + 2) Reorder the terms: 6(-1 + x) = 9(x + 2) (-1 * 6 + x * 6) = 9(x + 2) (-6 + 6x) = 9(x + 2) Reorder the terms: -6 + 6x = 9(2 + x) -6 + 6x = (2 * 9 + x * 9) -6 + 6x = (18 + 9x) Solving -6 + 6x = 18 + 9x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9x' to each side of the equation. -6 + 6x + -9x = 18 + 9x + -9x Combine like terms: 6x + -9x = -3x -6 + -3x = 18 + 9x + -9x Combine like terms: 9x + -9x = 0 -6 + -3x = 18 + 0 -6 + -3x = 18 Add '6' to each side of the equation. -6 + 6 + -3x = 18 + 6 Combine like terms: -6 + 6 = 0 0 + -3x = 18 + 6 -3x = 18 + 6 Combine like terms: 18 + 6 = 24 -3x = 24 Divide each side by '-3'. x = -8 Simplifying x = -8</span>

8 0

3 years ago

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A metallurgist has an alloy with 5% titanium and an alloy with 30% titanium. He needs 100 grams of an alloy with 15% titanium. H

andrey2020 [161]

Let us convert the percentages to decimal format first.. so 5% is just 5/100 or 0.05 and 15% is just 15/100 or 0.15

so hmmm, so, let's say it needs "x" amount and "y" amount of each respectively, so, whatever "x" and "y" are, they must add up to 100, and whatever their concentration is, must add up to what the mixture yields

thus

$\bf \begin{array}{lccclll}
&amount&concentration&
\begin{array}{llll}
concentrated\\
amount
\end{array}\\
&-----&-------&-------\\
\textit{5\% alloy}&x&0.05&0.05x\\
\textit{30\% alloy}&y&0.30&0.3y\\
-----&-----&-------&-------\\
mixture&100&0.15&15
\end{array}
\\\\\\
\begin{cases}
x+y=100\implies \boxed{y}=100-x\\
0.05x+0.3y=15\\
----------\\
0.5x+0.3\left( \boxed{100-x} \right)=15
\end{cases}$

solve for "x"

what's "y"? well, y = 100 - x

4 0

3 years ago