First, a Word From Your Producers Jon and Tanner.

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Presentation transcript:

First, a Word From Your Producers Jon and Tanner

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

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.

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

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

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

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

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.

Graph

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

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

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

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

Thank You!! From Jon and Tanner