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First, a Word From Your Producers Jon and Tanner

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Tanner and Jon are coaches for a basketball and a soccer team. There are 7 kids on the basketball team and 11 kids on the soccer team. They have $1000 to spend on at least 11 soccer balls and 7 basketballs. Each Ultra-basketball costs $50. Each Ultra-soccer ball costs $30. We need to buy as many balls as we can with our money. By Tanner and Jon

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Substitution x+y>25 (equation 1) -x y>25-x 50x+30(25-x)<1000 (equation 2) In this section, we converted the first equation into slope-intercept form and substituted it into the second equation for y.

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Substitution 50x+30(25-x)<1000 (equation 2) 50x+750-30x<1000 20x+750<1000 -750 20x< 250 Here, we distributed and combined like terms.

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Substitution 20x< 250 20 x < 12.5 In this part of the process, we just divided to find out what just a single x equaled.

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Substitution (cont’d) 12.5+y>25 -12.5 y>12.5 We rounded x down to 12 and y up to 13 because there are more people on the soccer team and you can’t buy half of a basketball or soccer ball, even if they are Ultra-basketballs and Ultra-Soccer balls

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Table XYMoney (Yes or No) Meet requirement? 511580 (Y)N 711680 (Y)Yes 712710 (Y)Yes 713740 (Y)Yes 714770 (Y)Yes 715800 (Y)Yes 716830 (Y)Yes 717860 (Y)Yes 718890 (Y)Yes 719920 (Y)Yes 720950 (Y)Yes 721980 (Y)Yes

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Table (cont’d) XYMoney (Y or N) Meet Requirements? 7221010 (N)Yes 8191030 (N)Yes 9121050 (N)Yes 10121070 (N)Yes 712710 (Y)Yes 812760 (Y)Yes 912810 (Y)Yes 1012860 (Y)Yes 1112910 (Y)Yes 12 960 (Y)Yes 13121010 (N)Yes 12*13*990 (Y)*Yes* The rows in bold are the ones where the cross of the lines would be, and the best one is x=12 and y=13, which is just under the budget, but higher than any of the others within the budget, and meets all requirements.

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Graph

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Elimination 50x+30y=1000 -50(x+y)=(25)-50 -50x-50y=-1250 Here we multiplied both sides of the equation by -50 so that it will cancel out the x variable when we add the equations together

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Elimination -50x-50y=-1250 50x+30y=1000 -20y=-250 Here, we added the equations together to get an easier equation.

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Elimination -20y=-250 -20 y=12.5 In this part, we divided each side by -20 to get a singular y variable.

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Elimination x+12.5=25 -12.5 -12.5 x=12.5 Now we just substituted the 12.5 in for y and found the value of x.

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Thank You!! From Jon and Tanner

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1 MA 1128: Lecture 09 – 6/08/15 Solving Systems of Linear Equations.

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