1. **Problem 27:** Kevin, Arya, and Mark share a total of 430. Given: - Kevin's share = $\frac{1}{4}$ of Arya's share - Mark's share = 85 - Total = 430 2. **Step 1: Define variables** Let Arya's share be $A$. Then Kevin's share is $\frac{1}{4}A$. Mark's share is 85. 3. **Step 2: Write the equation for total amount** $$A + \frac{1}{4}A + 85 = 430$$ 4. **Step 3: Simplify the equation** Combine like terms: $$A + \frac{1}{4}A = \frac{4}{4}A + \frac{1}{4}A = \frac{5}{4}A$$ So, $$\frac{5}{4}A + 85 = 430$$ 5. **Step 4: Solve for $A$** Subtract 85 from both sides: $$\frac{5}{4}A = 430 - 85 = 345$$ Multiply both sides by $\frac{4}{5}$: $$A = 345 \times \frac{4}{5} = 345 \times 0.8 = 276$$ 6. **Step 5: Find Kevin's share** $$K = \frac{1}{4}A = \frac{1}{4} \times 276 = 69$$ 7. **Answer for Problem 27:** - Arya's share = 276 - Kevin's share = 69 --- 8. **Problem 28:** A shopkeeper is packing 270 cans in boxes, each box holds 30 cans. He is packing the 151st can. Find which box he is packing. 9. **Step 1: Understand the problem** Each box holds 30 cans. We want to find the box number for the 151st can. 10. **Step 2: Calculate the box number** Divide the can number by cans per box: $$\frac{151}{30} = 5.0333...$$ Since the 151st can is in the 6th box (because the first 5 boxes hold 150 cans), we take the ceiling of the division: $$\text{Box number} = \lceil 5.0333... \rceil = 6$$ 11. **Answer for Problem 28:** - The 151st can is in box number 6.