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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 x< x+750< x< 250 Here, we distributed and combined like terms.

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Substitution 20x< 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> 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? (Y)N (Y)Yes (Y)Yes (Y)Yes (Y)Yes (Y)Yes (Y)Yes (Y)Yes (Y)Yes (Y)Yes (Y)Yes (Y)Yes

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Table (cont’d) XYMoney (Y or N) Meet Requirements? (N)Yes (N)Yes (N)Yes (N)Yes (Y)Yes (Y)Yes (Y)Yes (Y)Yes (Y)Yes (Y)Yes (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= (x+y)=(25) x-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= x+30y= y=-250 Here, we added the equations together to get an easier equation.

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Elimination -20y= 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= 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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