a student sells small and large greeting cards decorated at a craft fair. The small cards coast 3 dollars per card, and the large cards coast 5 dollars per card. The student collects 95 for selling a total of 25 cards. what are the variables what is the system how do you graph it how many of each card did the student sell please and thank you

Question

17-05-2014
Mathematics

Answered

a student sells small and large greeting cards decorated at a craft fair. The small cards coast 3 dollars per card, and the large cards coast 5 dollars per card. The student collects 95 for selling a total of 25 cards. what are the variables what is the system how do you graph it how many of each card did the student sell please and thank you

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Аноним Аноним · Answer 1 · 2014-05-17T19:52:22-04:00

[tex]x-the\ small\ cards\\y-the\ large\ cards\\\\ \left\{\begin{array}{ccc}3x+5y=95\\x+y=25\end{array}\right\\\left\{\begin{array}{ccc}5y=-3x+95&/:5\\y=-x+25\end{array}\right\\\left\{\begin{array}{ccc}y=-\frac{3}{5}x+19\\y=-x+25\end{array}\right\\\\----------------------[/tex]

[tex]y=-\frac{3}{5}x+19\\\\for\ x=0\to y=-\frac{3}{5}\cdot0+19=19\to A(0;\ 19)\\for\ x=10\to y=-\frac{3}{5}\cdot10+19=-6+19=13\to B(10;\ 13)\\----------------------------\\\\y=-x+25\\\\for\ x=0\to y=-0+25=25\to C(0;\ 25)\\for\ x=10\to y=-10+25=15\to D(10;\ 15)\\----------------------------\\\\a\ graph\ on\ the\ picture\\\\Answer:x=15\ and\ y=10.[/tex]