Could someone please check my answers?

Question

(I need help understanding this question..) 1. Three students played a game in which two of them won and one lost on each play. The person who lost had to subtract the sum of the winners’ scores from his own score. The winners doubled their scores. The three students played three times, each winning twice and losing once. At the end, each player had 40 points. How many points did each player have to start?

2. Three hundred forty five teams are beginning a single-elimination basketball tournament. One loss eliminates a team from the tournament. How many games must be played to determine a champion?

ANSWER: 345 games. If two teams play and one team loses, the winning team goes on and a champion would be determined during the final game.

3. A number is multiplied by 3. Then 8 is added to the product. The result is 50. What is the number? ANSWER: 3 times 14 equals 42. 42 plus 8 equals 50. 3 was the number used

4. The High School used 2000 gal mo

4. 5.The High School used 2000 gal more of heating oil than the elementary school. Together the schools used 76,000 gal of oil. How much oil did the high school use?

76,000 minus 2000 equals 74,000. 74,000 gallons of heating oil was used by the high school.

Thank you for the help! Could you please explain how you came up with the answer for #1?

Answer 1

#1 -- work backwards.

A = 40
B = 40
C = 40

Assume C lost the last round, A & B won. Then you have to divide A & B by 2. 40/2 = 20 so A = 20 and B = 20 at the beginning of the round. To determine C, you have to find a number where if you subtract A & B (values at the beginning of the round) you'll be left with 40. C - 20 -20 = 40 or C = 80.

Now do the same thing for the next 2 steps... Assume B lost 2nd round. Divide the #s for A & C above by 2. A = 20/2 = 10 and C = 80/2 = 40. Then B - 10 - 40 = 20 (see above; we said B has to = 20 in last round) or B = 70.

Last assume A lost 1st round. Divide B & C by 2... B = 70/2 = 35 and C = 40/2 =20. A - 35 - 20 = 10 or A = 65.

If working backwards doesn't make sense, look at it going forwards:

A B C
65 35 20 (A loses -- 65-35-20; double B & C)
10 70 40 (B loses -- 70-10-40; double A & C)
20 20 80 (C loses -- 80-20-20; double A & B)
40 40 40

#2 -- you need to play 344 games to eliminate 344 teams and leave one team undefeated....think about the first round... you'll get rid of 1/2 the teams. 345 divided by 2 is 172 with a remainder of 1. You'd have played 172 games and have 173 teams left. Do the same thing over & over until you are left with 2 teams (173 divided by 2 = 86 remainder of 1 so 86 games played, 87 teams left... etc.). Once you get down to 2 teams remaining, you play one game and have one team (the champ) left. Add up all the games played from your calculations and you should get 344.

#3... I think you have the math right but aren't giving the correct answer. YOu say 3 x 14 +8 = 50. The question says a number was multiplied by 3 and it's product added to 8. Your answer should be the number that was multiplied by 3, not 3 itself. You've given the answer 3 x 3 + 8 = 50, which is not a true statement.

#4 -- Does your answer make sense? If the HS uses 74000 you are saying the ES uses 72000 (2000 less). Together they'd use 146,000! Obviously that's not what the question tells you.

If they used the same amount, they'd each use 37,000 (74,000/2 = 37,000). The HS used 2000 more than the ES. So HS used 39,000 and ES used 35,000.

Or if you know how to do algebra:

E + H = 74000
H = E + 2000

Then you can substitute the E + 2000 into the H in the first equation and solve for E.

Answer 2

number 2 is wrong...
you would need 344 games, other wise there would'n't be a champion.
each player had 13 points for #1
#4 is right
#3 is correct

Answer 3

rethink #3--it's 3 times "a number". The number is actually 14, because it is the number being multiplied by the three.