Scenario: Geometry & Age Problems - Learn to solve complex real-world problems using equations!
A rectangle has a perimeter of 48 cm. The length is 6 cm more than the width. Find the length and width of the rectangle.
Setting up the equation:
Let x = width, then length = x + 6
Perimeter = 2(length + width)
48 = 2((x + 6) + x)
Step 1: Simplify inside parentheses
48 = 2((x + 6) + x) = 2(2x + 6)
Step 2: Distribute
48 = 4x + 12
Step 3: Subtract 12 from both sides
36 = 4x
Step 4: Divide by 4
x = 9 (width)
Length = 9 + 6 = 15 cm
A mother is 36 years old and her daughter is 9 years old. In how many years will the mother be 4 times as old as her daughter?
Setting up the equation:
Let x = number of years from now
Mother's age in x years: 36 + x
Daughter's age in x years: 9 + x
36 + x = 4(9 + x)
Step 1: Distribute
36 + x = 4(9 + x) = 36 + 4x
Step 2: Subtract x from both sides
36 = 36 + 3x
Step 3: Subtract 36 from both sides
0 = 3x, so x = 0
Answer: The mother is already 4 times as old as her daughter right now!
Two cars start from the same point and travel in opposite directions. One car travels at 50 km/h and the other at 40 km/h. How long will it take for them to be 180 km apart?
Setting up the equation:
Let t = time in hours
Distance = Speed × Time
Total distance apart = 50t + 40t = 90t
90t = 180
Step 1: Divide both sides by 90
90t = 180
t = 180 ÷ 90 = 2
Answer: It will take 2 hours for the cars to be 180 km apart.
A triangle has a perimeter of 30 cm. The first side is 8 cm, the second side is 2 cm longer than the third side. Find all three side lengths.
Your calculation:
Tom is 5 years older than his sister. In 3 years, he will be twice as old as she is now. How old is Tom now?
Your calculation: