8. hockey teams receive 2 points when they win and 1 point when they tie?

Question

one season, a team won a championship with 66 points. the won 12 more games than they tied. how many wins and how many ties did the team have?
tie__?
win__?

12. bay-side insurance offers 2 health plans. under plan A, Gina would have to pay the first 60$ of her med bills, plus 40% of the rest. under plan B, Gina would pay the first 90$, but only pay 30% of the rest. for what amount of med bill will B save Gina money?
assume she has over 90$ in bills.
Gina would save with plan B if she had more than __$ in bills.

aclotm · Accepted Answer

I'll do the first one, and hopefully this might get you started.
Set up an equation, letting x be the number of ties for a team. That means x+12 represents the number of wins since you need 12 more wins than ties. Now take the points into account: 2 for a win, so 2(x+12) and 1 for ties, so 1(x). This will equal your total points, which is 66

2(x+12) + 1(x) = 66
2x + 24 + x = 66
3x = 42
x = 14

This means the hockey team ties 14 games and wins 14 + 12 = 26 games.
Check your answer to make sure: 2(26) + 1(14) = 52 + 14 = 66 games

Ian · Answer

let
x= number of ties
y= number of wins
the total number of points from ties are x*1
the total number of points from wins are y*2
they had 66 points total, so...
66=x+2y
and also we are given
y=x+12
so, 66=x+2*(x+12)
66=3x+24
42=3x
x=14
and y=14+12=26
so they had 14 ties and 26 wins

The next one...
Let y= total amount of the bill
for  plan A
if y>60, she pays 60+0.40*(y-60)
=36+.4y

for plan B
if y>90, she pays 90+0.30*(y-90)
=63+.3y

since we assume y>90 then both hold true
so we can set them equal to see where the point at which one becomes greater than the other
so, 36+.4y=63+.3y
27=.1y
y=270
so if she had more than $270 in bills, plan B would be better.

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8. hockey teams receive 2 points when they win and 1 point when they tie?

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