Question

Tommy is using a bucket to collect nuts from a nut tree. He then dumps the bucket into a barrel for shipping of the nuts. He notices that 1 over 4 bucket of nuts fills 2 over 3 of the barrel.

Part A: Write and solve an equation to find the amount of nuts that will fill the entire barrel. Show your work. (8 points)

Part B: Explain your answer in words. (2 points)

Answer 1

• 3/8 bucket

Explanation:

Given that 1/4 bucket of nuts fills 2/3 of the barrel

PART A

To find the amount of nuts that fills entire basket we can put this as:

• 1/4 bucket → 2/3 barrel
• x bucket → 1 barrel

Use cross-multiplication to find the value of x:

• x×2/3 = 1×1/4
• x = 1/4 ÷ 2/3
• x = 1/4×3/2
• x = 3/8 bucket

PART B

• Using the bucket to barrel ratio to solve the problem. Having the number of required buckets as x and considering full barrel as 1 helps to find the value of x.