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18 Aug 2022, 05:32
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On a 2022 World Cup De Bruyne, Ronaldo, Mbappe and Messi together scored x goals. Out of these, 27 goals were not scored by De Bruyne, 22 goals were not scored by Ronaldo, 20 goals were not scored by Mbappe and 18 goals were not scored by Messi. How many goals did Messi score ?
A. \(7\)
B. \(9\)
C. \(11\)
D. \(13\)
E. \(29\)
A. \(7\)
B. \(9\)
C. \(11\)
D. \(13\)
E. \(29\)
18 Aug 2022, 05:32
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Official Solution:
On a 2022 World Cup De Bruyne, Ronaldo, Mbappe and Messi together scored x goals. Out of these, 27 goals were not scored by De Bruyne, 22 goals were not scored by Ronaldo, 20 goals were not scored by Mbappe and 18 goals were not scored by Messi. How many goals did Messi score ?
A. \(7\)
B. \(9\)
C. \(11\)
D. \(13\)
E. \(29\)
Say the number of goals scored by De Bruyne, Ronaldo, Mbappe and Messi be \(a, \ b, \ c,\) and \(d\), respectively. Then we'd have:
Sum the above four equations:
Since \(x = a + b + c + d\) (we are told that together they scored \(x\) goals), then:
Hence, Messi scored:
Answer: C
On a 2022 World Cup De Bruyne, Ronaldo, Mbappe and Messi together scored x goals. Out of these, 27 goals were not scored by De Bruyne, 22 goals were not scored by Ronaldo, 20 goals were not scored by Mbappe and 18 goals were not scored by Messi. How many goals did Messi score ?
A. \(7\)
B. \(9\)
C. \(11\)
D. \(13\)
E. \(29\)
Say the number of goals scored by De Bruyne, Ronaldo, Mbappe and Messi be \(a, \ b, \ c,\) and \(d\), respectively. Then we'd have:
27 goals were not scored by De Bruyne: \(27 = x - a\):
22 goals were not scored by Ronaldo: \(22 = x - b\)
20 goals were not scored by Mbappe: \(20 = x - c\)
18 goals were not scored by Messi: \(18 = x - d\)
22 goals were not scored by Ronaldo: \(22 = x - b\)
20 goals were not scored by Mbappe: \(20 = x - c\)
18 goals were not scored by Messi: \(18 = x - d\)
Sum the above four equations:
\(87 = 4x - a - b - c - d\)
Since \(x = a + b + c + d\) (we are told that together they scored \(x\) goals), then:
\(87 = 4x - x\);
\(x=29\)
\(x=29\)
Hence, Messi scored:
\(18 = x - d\);
\(18 = 29 - d\);
\(d=11\)
\(18 = 29 - d\);
\(d=11\)
Answer: C
General Discussion
08 Jan 2025, 09:58
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(x-22)+(x-27)+(x-20)+(x-18) = x
3x = 87
x = 29
Messi = x-18 = 29-18 = 11.
3x = 87
x = 29
Messi = x-18 = 29-18 = 11.
