waigaK

2021-08-18

Twelve gallons of a salt solution consists of $35\mathrm{%}$ salt. It is the result of mixing a $55\mathrm{%}$ solution with a $25\mathrm{%}$ solution. How many gallons of each of the solutions was used? Let $x=$ the number of gallons of the $55\mathrm{%}$ solution and $y=$ the number of gallons of the $25\mathrm{%}$ solution. The corresponding modeling system is $\left\{\begin{array}{l}x+y=12\\ 0.55x+0.25y=0.35\left(12\right)\end{array}$ Solve the system by using the method of substitution and what is the ordered pair?

Lacey-May Snyder

Step 1
Given system is $x+y=12\left(1\right)$
$0.55x+0.25y=0.35\left(12\right)\left(2\right)$
We solve this system using substitution
Step 2
From $\left(1\right)y=12-x\left(3\right)$
We substitute $y=12-x$ in (2) we get
$0.55x+0.25\left(12-x\right)=0.35x\left(12\right)$
$⇒0.55x+3-0.25x=4.2$
$⇒0.3x=4.2-3$
$⇒0.3x=1.2$
$⇒x=\frac{1.2}{0.3}=\frac{\frac{12}{10}}{\frac{3}{10}}=\frac{12}{10}×\frac{10}{3}=4$
From (3) $y=12-4=8$
Hence the solution $\left(x,y\right)=\left(4,8\right)$

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