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2 years ago

A sweater cost$12 more than a shirt.together they cost$46.what was the price of the shirt

Mathematics

2 answers:

Dmitry [639]2 years ago

6 0

The shirt cost 34 dollars.

alina1380 [7]2 years ago

3 0

Make the shirt equal x, and so the sweater is x + 12. Together they equal 46, so your equation is x + x + 12 = 46, which simplifies to 2x + 12 = 46. Subtract 12 from both sides, and you have 2x = 34. Divide both sides by two, and you have x = 17. The shirt is $17.

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See explanation

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Let x be the number of spade shovels, y -the number of flat shovels and z - the number of square showels sold that day.

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b) In matrix form this is

$\left(\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 16&9.60&12.80\end{array}\right)\cdot \left(\begin{array}{c}x\\y\\z\end{array}\right)=\left(\begin{array}{c}80\\0\\1,072\end{array}\right)$

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$\left\|\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 16&9.60&12.80\end{array}\right\|=0-32+9.60-0+19.20-12.80=-16$

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$\left\|\begin{array}{ccc}80&1&1\\ 0&0&-2\\ 1,072&9.60&12.80\end{array}\right\|=0-2,144+0-0+1,536-0=-608$

$\left\|\begin{array}{ccc}1&80&1\\ 1&0&-2\\ 16&1,072&12.80\end{array}\right\|=0-2,560+1,072-0+2,144-1,024=-368$

$\left\|\begin{array}{ccc}1&1&80\\ 1&0&0\\ 16&9.60&1,072\end{array}\right\|=0+0+768-0-0-1,072=-304$

So,

$x=\dfrac{-608}{-16}=38\\ \\y=\dfrac{-368}{-16}=23\\ \\z=\dfrac{-304}{-16}=19$

e) If the store doubled all prices and inventory, then the new matrix is

$\left(\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 32&19.20&25.60\end{array}\right)\cdot \left(\begin{array}{c}x\\y\\z\end{array}\right)=\left(\begin{array}{c}160\\0\\2,144\end{array}\right)$

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