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Digiron [165]
3 years ago
9

Karlie painted a portrait. The height of the portrait measures 14 inches. The width is half as long as the height. What is the a

rea of the portrait
Mathematics
2 answers:
natima [27]3 years ago
7 0
The answer is 98 because half of 14 is 7 (14/2). And since 10*7=70 and 4*7=28, 70+28=98. There is your answer. And explained.
NISA [10]3 years ago
6 0
14 times 7, so 98 square inches

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<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B10%28x%20-%20y%29%20-%204%281%20-%20x%29%7D%7B3%7D%20%20%3D%20y" id="TexFormula1"
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so first off, let's simplify both equations, starting off by multiplying both sides by the LCD of all fractions, to do away with the denominators.


\bf \cfrac{10(x-y)-4(1-x)}{3}=y\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{10(x-y)-4(1-x)=3y} \\\\\\ 10x-10y-4+4x=3y\implies \boxed{14x-13y=4} \\\\[-0.35em] ~\dotfill\\\\ 7+x-\cfrac{x-3y}{4}=2x-\cfrac{y+5}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( 7+x-\cfrac{x-3y}{4} \right)=12\left( 2x-\cfrac{y+5}{3} \right)} \\\\\\ 84+12x-3(x-3y)=24x-4(y+5) \\\\\\ 84+12x-3x+9y=24x-4y-20\implies \boxed{-15x+13y=-124}


now, let's do some elimination on those two simplified equations.


\bf \begin{array}{cllcl} 14x&-13y&=&4\\ -15x&+13y&=&-124\\\cline{1-4} -x&&=&-120 \end{array}~\hfill x=\cfrac{-120}{-1}\implies \blacktriangleright x=120 \blacktriangleleft \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{14(120)-13y=4}\implies 1680-13y=4\implies 1680-4=13y \\\\\\ 1676=13y\implies \blacktriangleright \cfrac{1676}{13}=y \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( 120~,~\frac{1676}{13} \right)~\hfill

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