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jenyasd209 [6]
3 years ago
13

13x+2y=1 5x−2y=−19 x= y=

Mathematics
1 answer:
ivanzaharov [21]3 years ago
6 0
+\underline{\left\{\begin{array}{ccc}13x+2y=1\\5x-2y=-19\end{array}\right}\ \ \ |\text{add both sides of equations}\\.\ \ \ \ \ 18x=-18\ \ \ \ |:18\\.\ \ \ \ \ \ x=-1\\\\\text{substitute the value of x to the first equation}\\\\13(-1)+2y=1\\-13+2y=1\ \ \ \ |+13\\2y=14\ \ \ \ |:2\\y=7\\\\\text{Answer:}\  \left \{ {{x=-1} \atop {y=7}} \right.
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3 years ago
The coffee Lily likes is composed of 97.3% water and 2.7% cocoa. The coffee John likes is composed of 96% water and 4% cocoa. Ho
mestny [16]

30 ounces of the coffee John likes consists of

  • 0.96\cdot30=28.8 ounces of water
  • 0.04\cdot30=1.2 ounces of cocoa

To this mixture we're adding x ounces of water, so that the new mix has a total volume of 30+x ounces and matches the composition of the coffee Lily likes. This means it would consist of

  • 0.973\cdot(30+x)=28.8+x ounces of water
  • 0.027\cdot(30+x)=1.2 ounces of cocoa (same amount of cocoa as before because pure water is being added)

Solve for x:

0.973(30+x)=28.8+x\implies29.12+0.973x=28.8+x

\implies0.39=0.027x

\implies x\approx14.4

###

Just to confirm: the new mixture consists of

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  • 1.2+0=1.2 ounces of cocoa

giving a total volume of 43.2+1.2=44.4 ounces of coffee, and \dfrac{43.2}{44.4}\approx0.973, as required.

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