MATH - GRADE 9
Read and analyze the following words problems, Show your solution.
1. For every litter of petrol, one car travels x km and another car travels 5 km more than the first. If the first car uses 4 liters more than second car in converting 400 km. What is the value of x?
2. 780 students stand in rows and columns. Each row has equal number of students and each column had equal number of students. If the number of students in each row is 4 more than the number of rows, Find the number of students in each row.
Read and analyze the following words problems, Show your solution.
1. For every litter of petrol, one car travels x km and another car travels 5 km more than the first. If the first car uses 4 liters more than second car in converting 400 km. What is the value of x?
2. 780 students stand in rows and columns. Each row has equal number of students and each column had equal number of students. If the number of students in each row is 4 more than the number of rows, Find the number of students in each row.
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Answer:
Car A travels 400 km using 4 litres more than car B.
Car A travels x km per litre.
Car B travels x+5 km per litre.
Car A consumes 400/x litres of fuel.
Car B consumes 400/(x+5) litres of fuel.
Therefore:
400/x - 400/(x+5) = 4
400.(x+5) - 400.x = 4.x.(x+5)
400x + 2000 - 400x = 4x^2 + 20x
x^2 + 5x - 500 = 0
x = 20, -25
Presumably negative results are inadmissible in the real world.
x = 20
Car A ttravels 20 km per litre (nice car).
Car B travels 25 km per litre (even better).
Testing
400/20 - 400/25 = 20 - 16 = 4
Car B travels 25 km per litre (even better).
Testing
400/20 - 400/25 = 20 - 16 = 4