document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191395>Question 1191395</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Translate to a system of inequalities and solve.<BR>\n" );
document.write( "Jocelyn is pregnant and needs to eat at least 400 more calories a day than usual. When buying groceries one day with a budget of $15 for the extra food, she buys bananas that have 90 calories each and chocolate granola bars that have 150 calories each. The bananas cost $0.35 each and the granola bars cost $2.50 each.<BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "Write a system of inequalities to model this situation. (Let b represent the bananas bought and let g represent the number of granola bars bought. Enter your answers as a comma-separated list of inequalities.)<BR>\n" );
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document.write( "(b)<BR>\n" );
document.write( "Graph the system.\r<BR>\n" );
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document.write( "(c)<BR>\n" );
document.write( "Could she buy 6 bananas and 6 granola bars?\r<BR>\n" );
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document.write( "(d)<BR>\n" );
document.write( "Could she buy 3 bananas and 3 granola bars? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849216 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **(a) System of Inequalities**\r<BR>\n" );
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document.write( "Let 'b' represent the number of bananas and 'g' represent the number of granola bars.\r<BR>\n" );
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document.write( "* **Calorie Inequality:** Jocelyn needs at least 400 extra calories.<BR>\n" );
document.write( "   90b + 150g ≥ 400\r<BR>\n" );
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document.write( "* **Budget Inequality:** Jocelyn has a budget of $15.<BR>\n" );
document.write( "   0.35b + 2.50g ≤ 15\r<BR>\n" );
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document.write( "* **Non-Negative Inequalities:**  Jocelyn can't buy a negative number of bananas or granola bars.<BR>\n" );
document.write( "   b ≥ 0<BR>\n" );
document.write( "   g ≥ 0\r<BR>\n" );
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document.write( "Therefore, the system of inequalities is:  **90b + 150g ≥ 400, 0.35b + 2.50g ≤ 15, b ≥ 0, g ≥ 0**\r<BR>\n" );
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document.write( "**(b) Graphing the System**\r<BR>\n" );
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document.write( "I can't draw a graph here, but I'll describe how to graph it:\r<BR>\n" );
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document.write( "1. **Convert to Slope-Intercept Form (for easier graphing):**<BR>\n" );
document.write( "   * Calorie Inequality: 150g ≥ -90b + 400  =>  g ≥ (-3/5)b + (8/3)<BR>\n" );
document.write( "   * Budget Inequality: 2.50g ≤ -0.35b + 15  => g ≤ (-7/50)b + 6\r<BR>\n" );
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document.write( "2. **Plot the Lines:**<BR>\n" );
document.write( "   * For g ≥ (-3/5)b + (8/3), plot the line g = (-3/5)b + (8/3).  Since it's \"greater than or equal to,\" shade the area *above* this line.<BR>\n" );
document.write( "   * For g ≤ (-7/50)b + 6, plot the line g = (-7/50)b + 6. Since it's \"less than or equal to,\" shade the area *below* this line.<BR>\n" );
document.write( "   * Also, remember b ≥ 0 and g ≥ 0, which means you're only considering the first quadrant (positive b and g values).\r<BR>\n" );
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document.write( "3. **Solution Region:** The solution region is where all the shaded areas overlap.  This represents the possible combinations of bananas and granola bars that meet Jocelyn's requirements.\r<BR>\n" );
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document.write( "**(c) 6 Bananas and 6 Granola Bars?**\r<BR>\n" );
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document.write( "* Calories: 90(6) + 150(6) = 540 + 900 = 1440 calories (meets the calorie need)<BR>\n" );
document.write( "* Cost: 0.35(6) + 2.50(6) = 2.10 + 15 = $17.10 (exceeds the budget)\r<BR>\n" );
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document.write( "No, she could not buy 6 bananas and 6 granola bars because it exceeds her budget.\r<BR>\n" );
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document.write( "**(d) 3 Bananas and 3 Granola Bars?**\r<BR>\n" );
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document.write( "* Calories: 90(3) + 150(3) = 270 + 450 = 720 calories (meets the calorie need)<BR>\n" );
document.write( "* Cost: 0.35(3) + 2.50(3) = 1.05 + 7.50 = $8.55 (within the budget)\r<BR>\n" );
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document.write( "Yes, she could buy 3 bananas and 3 granola bars.<BR>\n" );
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