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A competition requires teams to attempt 10 long jumps and 5 high jumps
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02 Sep 2019, 23:14
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82% (02:52) correct 18% (02:10) wrong based on 17 sessions
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Competition Mode Question A competition requires teams to attempt 10 long jumps and 5 high jumps. Each successful long jump is worth the same number of points, and each successful high jump is worth the same number of points. Team A completed all 15 jumps, receiving 20 points. Team B succeeded in only 8 long jumps and 2 high jumps, earning 10 points. Team C missed 2 long jumps and successfully completed all the high jumps. How many points did Team C score? (A) 12 (B) 13 (C) 15 (D) 18 (E) 19
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Re: A competition requires teams to attempt 10 long jumps and 5 high jumps
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03 Sep 2019, 00:12
Let points for a successful high jump be x and y be the points for a successful long jump. Then for team A: 20=10x+5y ..........(1) team B: 10=8x+2y equivalent to 5=4x+y ...(2) (2)*5 leads to 25=20x+5y .......(3) (3)(1) leads to 5=10x hence x=0.5 And we can get y = 3 when x=0.5 is substituted into (2) The points gotten by Team C = 5*3 =15, since they were only successful in completing all five high jumps. Hence the answer is C.
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Re: A competition requires teams to attempt 10 long jumps and 5 high jumps
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03 Sep 2019, 00:40
10 long jumps and 5 high jumps .....total 15 jumps Let x be long jump and y be high jump Team A completed all 15 jumps, receiving 20 points. => 10x+5y=20.............eq 1 Team B succeeded in only 8 long jumps and 2 high jumps, earning 10 points. => 8x+2y=10.............eq 2 Team C missed 2 long jumps and successfully completed all the high jumps.=> 8x+5y=?Solving eq 1 & 2 for x and y gives x=0.5 and y=3 Team C's points= 8(0.5)+5(3)= 4+15 =19...........Option E
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Re: A competition requires teams to attempt 10 long jumps and 5 high jumps
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03 Sep 2019, 01:47
A competition requires teams to attempt 10 long jumps and 5 high jumps. Each successful long jump is worth the same number of points, and each successful high jump is worth the same number of points. Team A completed all 15 jumps, receiving 20 points. Team B succeeded in only 8 long jumps and 2 high jumps, earning 10 points. Team C missed 2 long jumps and successfully completed all the high jumps. How many points did Team C score? 10L+5H=20 8L+2H=10 8L+5H=? solve by substitution we get L=1/2 H=3 therefore, 8(1/2)+5(3)=19 E



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Re: A competition requires teams to attempt 10 long jumps and 5 high jumps
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03 Sep 2019, 02:04
Let's x be points earned from each long jump, and y be points earned from each high jump.
Team A: completed all 15 jumps and receiving 20 points  10x + 5y = 20 (Equation 1) Team B: completed 8 long jumps, 2 high jumps  8x + 2y = 10 (Equation 2)
Solve the equation: x = 0.5, y = 3
Finding Team C points: completed 8 long jumps, 5 high jumps  8x + 5y = 8(0.5) + 5(3) = 19 points. > Answer E



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Re: A competition requires teams to attempt 10 long jumps and 5 high jumps
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03 Sep 2019, 03:31
Total number of jumps in competition = 10 + 5 = 15 where n(L) = 10 and n(H) = 5. To find = Total points of Team C. Given that there are three teams – Team A, Team B and Team C. Let L and H be the points per jumps or Long jumps and High jumps respectively. Team A: \(n(L) = 10\) & \(n(H) = 5\) and Points = 20 \(10L + 5H = 20\) \(2L + H = 4\) Eqn. ① Team B: \(n(L) = 8\) & \(n(H) = 2\) and Points = 10 \(8L + 2H = 10\) \(4L + H = 5\) Eqn. ② Team C: \(n(L) = 8\) & \(n(H) = 5\) and Points = ? Points = \(8L + 5H\) Since we have two variables and two equations we can solve for the variables. \(Eqn. ②  Eqn. gives 4L  2L + H – H = 5 – 4\) \(2L = 1\) \(L = ½\) Solving for H either equation gives \(H = 3\) Thus, \(8L + 5H = 8 * \frac{1}{2} + 5 * 3\) \(8L + 5H = 19\) Answer (E).
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Re: A competition requires teams to attempt 10 long jumps and 5 high jumps
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03 Sep 2019, 03:40
Quote: A competition requires teams to attempt 10 long jumps and 5 high jumps. Each successful long jump is worth the same number of points, and each successful high jump is worth the same number of points. Team A completed all 15 jumps, receiving 20 points. Team B succeeded in only 8 long jumps and 2 high jumps, earning 10 points. Team C missed 2 long jumps and successfully completed all the high jumps. How many points did Team C score?
(A) 12 (B) 13 (C) 15 (D) 18 (E) 19 [Q] 8x+5y=? [1] 10x+5y=20 [2] 8x+2y=10 [3:12] 2x+3y=10 [32] 6xy=0…6x=y [2] 8x+2y=10…8x+2(6x)=10…20x=10…x=0.5 [Q] 8x+5y=…8x+5(6x)=…38x=…38(0.5)=19 Answer (E)



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Re: A competition requires teams to attempt 10 long jumps and 5 high jumps
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03 Sep 2019, 06:34
IMO it's E, 19 We can make two equations by the question stem: 10L+5H=20 8L+2H=10 Solving these 2 we will get, H=3, L=0.5 Team C completed 8L and 5H which will total make 4+15=19 points.A competition requires teams to attempt 10 long jumps and 5 high jumps. Each successful long jump is worth the same number of points, and each successful high jump is worth the same number of points. Team A completed all 15 jumps, receiving 20 points. Team B succeeded in only 8 long jumps and 2 high jumps, earning 10 points. Team C missed 2 long jumps and successfully completed all the high jumps. How many points did Team C score? (A) 12 (B) 13 (C) 15 (D) 18 (E) 19
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A competition requires teams to attempt 10 long jumps and 5 high jumps
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Updated on: 08 Sep 2019, 01:02
We have two equations and two variables, looking to solve for the 2 variables. The first equation is \(10L + 5H = 20\), second equation is \(8L + 2H = 10\). We can multiply the second equation by 2.5 so that we can eliminate the variable \(H\), this gives \(10L = 5\) and \(L = 0.5\), thus \(H = 3\). The answer is \(8L + 5H = 4 + 15 = 19\), E. It would be good practice to try solving this in your head, the key here is to find a nice variable to eliminate and here we multiply the second equation by 2.5 to match the \(5H\) in the first equation.
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Re: A competition requires teams to attempt 10 long jumps and 5 high jumps
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03 Sep 2019, 22:46
given h+l=15 h=10 and l=5 also 10x+5y=20 8x+2y=10 find 8x+5y solve for x& y ; x= 0.5 and y=3 so 8x+5y= 19 IMO E
A competition requires teams to attempt 10 long jumps and 5 high jumps. Each successful long jump is worth the same number of points, and each successful high jump is worth the same number of points. Team A completed all 15 jumps, receiving 20 points. Team B succeeded in only 8 long jumps and 2 high jumps, earning 10 points. Team C missed 2 long jumps and successfully completed all the high jumps. How many points did Team C score?
(A) 12 (B) 13 (C) 15 (D) 18 (E) 19




Re: A competition requires teams to attempt 10 long jumps and 5 high jumps
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03 Sep 2019, 22:46






