Primary 6 Math Problem: Find Used Thread Length with Ratio and Unit Conversion

Question

Xinyi had 1.4 m of thread and Siti had 60 cm of thread. After they had used the same length of thread for their projects, the length of Xinyi's thread was 3 times the length of Siti's thread. What was the length of thread used by each girl? Give your answer in centimetres.

Accepted Answer

20 cm

Answer

Step 1: Convert Xinyi's thread length to centimetres to keep units consistent. Since 1 m = 100 cm, 1.4 m = 1.4 × 100 = 140 cm. Step 2: Let the length of thread used by each girl be $ x $ cm. After using the thread, Xinyi's remaining thread is $ 140 - x $ cm, and Siti's remaining thread is $ 60 - x $ cm. Step 3: Set up the equation based on the given relationship: $ 140 - x = 3(60 - x) $. Step 4: Expand and solve the equation: $ 140 - x = 180 - 3x $. Add $ 3x $ to both sides: $ 140 + 2x = 180 $. Subtract 140 from both sides: $ 2x = 40 $. Divide both sides by 2: $ x = 20 $. Alternative step (using unit difference method): Calculate the original length difference: 140 - 60 = 80 cm. The ratio of remaining threads is 3:1, so the difference in units is 3 - 1 = 2 units. 2 units = 80 cm, so 1 unit = 40 cm. Siti's remaining thread is 40 cm, so the used length is 60 - 40 = 20 cm.