First, a Word From Your Producers Jon and Tanner

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 -xy>25-x50x+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+750-30x<100020x+750<1000-750 -75020x< 250

Here, we distributed and combined like terms.

Substitution

20x< 25020 20x < 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>25-12.5 -12.5y>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

TableX Y Money (Yes

or No)Meet

requirement?

5 11 580 (Y) N

7 11 680 (Y) Yes

7 12 710 (Y) Yes

7 13 740 (Y) Yes

7 14 770 (Y) Yes

7 15 800 (Y) Yes

7 16 830 (Y) Yes

7 17 860 (Y) Yes

7 18 890 (Y) Yes

7 19 920 (Y) Yes

7 20 950 (Y) Yes

7 21 980 (Y) Yes

Table (cont’d)X Y Money (Y or N) Meet

Requirements?

7 22 1010 (N) Yes

8 19 1030 (N) Yes

9 12 1050 (N) Yes

10 12 1070 (N) Yes

7 12 710 (Y) Yes

8 12 760 (Y) Yes

9 12 810 (Y) Yes

10 12 860 (Y) Yes

11 12 910 (Y) Yes

12 12 960 (Y) Yes

13 12 1010 (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

0 5 10 15 20 25 300

5

10

15

20

25

30

0

25

12

25

0

13

First Equation (Crossing point)

Soccer ballsBasketballs

Elimination50x+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

Elimination-50x-50y=-125050x+30y=1000-20y=-250

Here, we added the equations together to get an easier equation.

Elimination-20y=-250-20 -20y=12.5

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

Eliminationx+12.5=25 -12.5 -12.5x=12.5

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

Thank You!!From Jon and Tanner