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The grade 8 learners decided to start living more healthily. They will either jog or cycle. There are 125 Grade 8 learners, and they jog and cycle in the ratio 3.2 Calculate how many learners participate in each sport?

Ask by Nunez Griffiths. in South Africa
Mar 12,2025

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Tutor-Verified Answer

Answer

75 learners jog and 50 learners cycle.

Solution

Let the number of learners who jog be \( j \) and those who cycle be \( c \). Given the ratio of joggers to cyclists is \( 3:2 \), we write: \[ \frac{j}{c} = \frac{3}{2} \] which implies: \[ j = \frac{3}{2}c \] We are also given that the total number of learners is 125: \[ j + c = 125 \] Substitute \( j = \frac{3}{2}c \) into the total: \[ \frac{3}{2}c + c = 125 \] Combine the terms: \[ \left(\frac{3}{2} + 1\right)c = 125 \] Convert 1 to \(\frac{2}{2}\) to sum easily: \[ \left(\frac{3}{2} + \frac{2}{2}\right)c = \frac{5}{2}c = 125 \] Solve for \( c \) by multiplying both sides by \(\frac{2}{5}\): \[ c = 125 \cdot \frac{2}{5} = 50 \] Now substitute \( c = 50 \) back into \( j = \frac{3}{2}c \): \[ j = \frac{3}{2} \cdot 50 = 75 \] Thus, the number of learners who jog is \( 75 \) and those who cycle is \( 50 \).

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To find out how many learners jog and how many cycle, we first need to understand the ratio of learners participating in these activities. The ratio of joggers to cyclists is 3:2, which means for every 5 learners (3 joggers + 2 cyclists), 3 will be joggers and 2 will be cyclists. To find the total number of parts in the ratio, we add the parts: 3 + 2 = 5 parts. Now, we can calculate how many learners each part represents by dividing the total number of learners (125) by the total parts (5): 125 ÷ 5 = 25 learners per part. Now we can calculate the number of learners for each activity: - Joggers: 3 parts × 25 learners/part = 75 learners - Cyclists: 2 parts × 25 learners/part = 50 learners So, 75 Grade 8 learners jog and 50 Grade 8 learners cycle.

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