Final answer:
To find the lengths of the two pieces of wire, set up an equation where the shorter piece is x cm and the longer piece is x + 10 cm. Solving the equation x + (x + 10) = 42 gives the lengths of 16 cm and 26 cm for the shorter and longer pieces, respectively.
Step-by-step explanation:
The student's question involves dividing a 42 cm piece of wire into two pieces where one piece is 10 cm longer than the other. To solve this, we let the length of the shorter piece be x cm. Therefore, the longer piece will be x + 10 cm. We can then set up the equation x + (x + 10) = 42 to represent the total length of the wire. Solving this equation:
- Combine like terms: 2x + 10 = 42
- Subtract 10 from both sides: 2x = 32
- Divide by 2 to find x: x = 16
This means the shorter piece is 16 cm and the longer piece is 16 + 10 = 26 cm.