Mathland High School held a festival to raise money for a local charity. One of
ID: 3100948 • Letter: M
Question
Mathland High School held a festival to raise money for a localcharity. One of the most popular events was a dunking tank where
students had a chance to dunk teachers.
When Mr. Rashanul went in the booth, four of his algebra students
each tried to dunk him. Each one took a different number of throws
before eventually hitting the target and sending Mr. Rashanul
plunging into the water.
Jorge took one less than twice as many throws as Shauna did.
Shauna took twice as many as Kenya did, and Toni took two less than
Jorge. The average number of throws for the four students was 4 and
1/2.
Use two different algebraic methods to figure out how many throws each student took. For
instance, you might solve it the first time with your variable representing the number of throws for
one of the students. The second time you could use a different student's throws as the variable or
you could use four variables, one for each student's throws. Do you get the same answer?
Be sure to show and explain your thinking and work.
Extra: Which of your methods do you think was easier? Why do you think so?
Explanation / Answer
I'm going to use the first letter of the kids' names so I don't have to clutter myself writing out the entire name. J = 2S - 1 S = 2K T = J - 2 (J + S + K + T)/4 = 4.5 So first I substituted for the three variables in the last equation to solve J. S = (J + 1)/2 K = S/2 = (J + 1)/4 T = J - 2 (J + (J+1)/2 + (J+1)/4 + J - 2)/4 = 4.5 Multiply both sides by 4 J + (J+1)/2 + (J+1)/4 + J - 2 = 18 then again Multiply both sides by 4 4J + 2J + 2 + J + 1 + 4J - 8 = 72 4J + 2J + J + 4J - 5 = 72 Add both sides by 5 4J + 2J + J + 4J = 77 11J = 77 J = 7 Remember I solved every variable in terms of J: S = (J + 1)/2 S = (7+1)/2 = 4 K = S/2 = (J + 1)/4 K = 4/2 = (7 + 1)/4 = 2 T = J - 2 T = 7 - 2 = 5 So, J = 7 S = 4 K = 2 T = 5