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Math Expert V
Joined: 02 Sep 2009
Posts: 58402
A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 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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Senior Manager  G
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Posts: 357
Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

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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  [#permalink]

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1
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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Manager  G
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Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

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1
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  [#permalink]

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1
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
Senior Manager  G
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Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

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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, $$8L + 5H = 8 * \frac{1}{2} + 5 * 3$$
 $$8L + 5H = 19$$

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

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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=?
 10x+5y=20
 8x+2y=10
[3:1-2] 2x+3y=10
[3-2] 6x-y=0…6x=y
 8x+2y=10…8x+2(6x)=10…20x=10…x=0.5
[Q] 8x+5y=…8x+5(6x)=…38x=…38(0.5)=19

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

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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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GMAT Tutor S
Joined: 17 Sep 2014
Posts: 198
Location: United States
GMAT 1: 780 Q51 V45 GRE 1: Q170 V167 A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

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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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Originally posted by TestPrepUnlimited on 03 Sep 2019, 07:44.
Last edited by TestPrepUnlimited on 08 Sep 2019, 01:02, edited 1 time in total.
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Re: A competition requires teams to attempt 10 long jumps and 5 high jumps  [#permalink]

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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   [#permalink] 03 Sep 2019, 22:46
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