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A construction company has three branches in Lima, Trujillo and Arequipa. The total number of executives in the three branches is 32. It is known that the number of executives living in Trujillo is 10 less than the number of executives in Lima. In addition, the number of executives in Lima exceeds by 4 the number of executives living in Arequipa and Trujillo combined. How many more executives live in the city of Lima than in Arequipa? It raises the System of Linear Equations and uses a Cramer method.

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Answer to a math question A construction company has three branches in Lima, Trujillo and Arequipa. The total number of executives in the three branches is 32. It is known that the number of executives living in Trujillo is 10 less than the number of executives in Lima. In addition, the number of executives in Lima exceeds by 4 the number of executives living in Arequipa and Trujillo combined. How many more executives live in the city of Lima than in Arequipa? It raises the System of Linear Equations and uses a Cramer method.

Expert avatar
Fred
4.4
118 Answers
L + T + A = 32
T = L - 10
L = A + T + 4

1. Substitute T = L - 10 into L + T + A = 32:
L + (L - 10) + A = 32
2L - 10 + A = 32
2L + A = 42

2. Substitute T = L - 10 into L = A + T + 4:
L = A + (L - 10) + 4
L = A + L - 6
0 = A - 6
A = 6

3. Substitute A = 6 into 2L + A = 42:
2L + 6 = 42
2L = 36
L = 18

4. Substitute L = 18 into T = L - 10:
T = 18 - 10
T = 8

5. Calculate the difference between executives in Lima and Arequipa:
L - A = 18 - 6 = 12

\text{El número de ejecutivos en Lima que exceden sobre Arequipa es:} \\12

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