5. Kelly's new snowboard is \( 120 \% \) longer than her old snowboard. If the new snowboard is 150 cm , how many centimeters long is her old snowboard?

To find the length of Kelly's old snowboard, we can set up the problem using the information given: 1. Let \( x \) be the length of the old snowboard in centimeters. 2. According to the problem, the new snowboard is \( 120\% \) longer than the old snowboard. This means that the new snowboard's length can be expressed as: \[ \text{New snowboard length} = \text{Old snowboard length} + 120\% \text{ of Old snowboard length} \] This can be rewritten as: \[ 150 = x + 1.2x \] 3. Combining the terms on the right side gives: \[ 150 = 2.2x \] 4. To find \( x \), we can solve for it by dividing both sides by \( 2.2 \): \[ x = \frac{150}{2.2} \] Now, let's calculate \( x \). Calculate the value by following steps: - step0: Calculate: \(\frac{150}{2.2}\) - step1: Convert the expressions: \(\frac{150}{\frac{11}{5}}\) - step2: Multiply by the reciprocal: \(150\times \frac{5}{11}\) - step3: Multiply: \(\frac{150\times 5}{11}\) - step4: Multiply: \(\frac{750}{11}\) Calculating \( x \) gives us: \[ x = \frac{150}{2.2} \approx 68.18 \] This can also be expressed as: \[ x = 68 \frac{2}{11} \text{ cm} \] Thus, the length of Kelly's old snowboard is approximately \( 68.18 \) cm or \( 68 \frac{2}{11} \) cm.