Question

!!MATH GENIUSES HELP ME!!

Bill and Theo played ice hockey for their high school team. Together they scored 90 goals in their four years on the team. The number of goals scored by Bill, squared, equals the number of goals that Theo scored.
How many goals did each player score?

A Bill scored 30 and Theo scored 60.
B Bill scored 41 and Theo scored 49.
C Bill scored 81 and Theo scored 9.
D Bill scored 9 and Theo scored 81.

Answer 1

D

Explanation:

Let x be Bill’s scores.

Let y be Theo’s scores.

x + y = 90

x² = y

Solve for x in the second equation.

x = √y

Put x as √y in the first equation and solve for y.

√y + y = 90

√y = 90 - y

y = (90 - y)²

y = - y² - 180y - 8100

0 = -y² - 181y - 8100

0 = (-y+81)(y-100)

-y+81=0

y = 81

y - 100 = 0

y = 100

100 does not work if we plug in to check, so y is 81.

y = 81

Put y as 81 in the first equation and solve for x.

x + 81 = 90

x = 9

Bill scored 9 goals and Theo scored 81.