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A competition requires teams to attempt 10 long jumps and 5 high jumps

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A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

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New post 29 Sep 2016, 19:07
1
1
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

76% (02:43) correct 24% (02:36) wrong based on 150 sessions

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this question comes from Prep4Gmat app

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  [#permalink]

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New post 29 Sep 2016, 20:24
lalania1 wrote:
this question comes from Prep4Gmat app

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


This is algebra problem in word form. Let L be points for long jump and H for high jump,
so A got 10 L + 5 H = 20 => 2 L + H = 4
B got 8 L + 2 H = 10 => 4 L + H = 5

C got 8 L + 5 H = ?

So multiply A by 6 and subtract B , 6(2 L + H ) - 4 L - H = 6 * 4 - 5 = 24 - 5 =19
Answer is E
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Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

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New post 01 Oct 2016, 10:14
step1: write down the formulas: 10L + 5 H = 20 and 8L + 2H = 10.
step2: before jumping into solution mode, identify what you are looking for. You are looking for 8L + 5H = ? or you can also say that 20 - 2L = ? in order to save some seconds and keep accuracy.
step3: simplify both formulas: 2L + H = 4 and 4L + H = 5 => H = 4 - 2L => replace into second formula => 4L + 4 - 2L = 5 => L = 0.5
step4: solve for 8L + 5H the long way or realize that 2L = 2(0.5) = 1 => 20 (all) - 1 (missing 2 Long jumps) = 19!
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Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

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New post 19 Oct 2016, 13:38
This problem can be solved with system of equations:

From Team A: 10x+5y = 20
From Team B: 8x+2y=10

Solve using whatever method you choose (i.e. substitution or elimination) --> x = 1/2 & y = 3

Team C: 8(1/2) + 5(3) = 19
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A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

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New post Updated on: 23 Jan 2019, 05:22
Solution:
Let the points for Long jump be “x”
Let the points for High jump be “y”.

Approach:
Team A: \(10x + 5y = 20\) -------------------- (1)
Team B: \(8x + 2y = 10\) ----------------------- (2)

Solving equation 1 and 2 we get x = 0.5 and y = 3

∴The total points scored by team \(C=(8 ×0.5+5 ×3 )\)= \(4+15\)=\(19.\)

So the correct answer option is “E”.

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Originally posted by Byjus on 27 Feb 2017, 04:07.
Last edited by Byjus on 23 Jan 2019, 05:22, edited 1 time in total.
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A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

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New post 02 Sep 2018, 07:56
For team A: 10l+ 5h= 20....(1)
For team B: 8l+2h=10...(2)
For team C: 8l+5h=?...(3)
Where l=long jump and h=high jump
Solving 1 and 2 we get l=.5 and h=3 so we get 19 as the points earned by team C
E is the correct choice.
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A competition requires teams to attempt 10 long jumps and 5 high jumps   [#permalink] 02 Sep 2018, 07:56
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