Question

violet, will, and xavier plant a total of 1235 trees. violet plants for 6 hours, will plants for 8 hours, and xavier plants for 7 hours. their planting rate is in proportion, with violet planting 16 trees for every 11 trees will plants and every 9 trees xavier plants. violet plants ___ trees in total.

Explanation:

Step1: Define ratio variables

Let Violet's planting rate be $16x$ trees/hour, Will's rate be $11x$ trees/hour, Xavier's rate be $9x$ trees/hour.

Step2: Calculate total trees equation

Total trees = (Violet's rate × hours) + (Will's rate × hours) + (Xavier's rate × hours)
$$16x \times 6 + 11x \times 8 + 9x \times 7 = 1235$$

Step3: Simplify left-hand side

$$96x + 88x + 63x = 1235$$
$$247x = 1235$$

Step4: Solve for x

$$x = \frac{1235}{247} = 5$$

Step5: Calculate Violet's total trees

Violet's total = $16x \times 6 = 16 \times 5 \times 6$

Answer:

480