martin decided to buy 2 bags of grapes weighing $5\frac{2}{3}$ pounds each, instead of the 3 bags weighing…

martin decided to buy 2 bags of grapes weighing $5\frac{2}{3}$ pounds each, instead of the 3 bags weighing $4\frac{1}{5}$ pounds each, because the bigger bags were on sale. did he end up with more grapes or less grapes by buying the bigger bags?\nhe ended up with about $\frac{1}{2}$ pound less grapes.\nhe ended up with about $\frac{1}{2}$ pound more grapes.\nhe ended up with about 1 pound less grapes.\nhe ended up with about 1 pound more grapes.

martin decided to buy 2 bags of grapes weighing $5\frac{2}{3}$ pounds each, instead of the 3 bags weighing $4\frac{1}{5}$ pounds each, because the bigger bags were on sale. did he end up with more grapes or less grapes by buying the bigger bags?\nhe ended up with about $\frac{1}{2}$ pound less grapes.\nhe ended up with about $\frac{1}{2}$ pound more grapes.\nhe ended up with about 1 pound less grapes.\nhe ended up with about 1 pound more grapes.

Answer

Explanation:

Step1: Calculate weight of 2 bigger bags

First, convert the mixed - number $5\frac{2}{3}$ to an improper fraction: $5\frac{2}{3}=\frac{5\times3 + 2}{3}=\frac{17}{3}$. Then the weight of 2 bags is $2\times\frac{17}{3}=\frac{34}{3}\approx11.33$ pounds.

Step2: Calculate weight of 3 smaller bags

Convert the mixed - number $4\frac{1}{5}$ to an improper fraction: $4\frac{1}{5}=\frac{4\times5+1}{5}=\frac{21}{5}$. Then the weight of 3 bags is $3\times\frac{21}{5}=\frac{63}{5} = 12.6$ pounds.

Step3: Find the difference

Subtract the weight of the 2 bigger bags from the weight of the 3 smaller bags: $\frac{63}{5}-\frac{34}{3}=\frac{63\times3 - 34\times5}{15}=\frac{189 - 170}{15}=\frac{19}{15}\approx1.27\approx1$ pound. Since $\frac{63}{5}>\frac{34}{3}$, he ended up with about 1 pound less grapes.

Answer:

He ended up with about 1 pound less grapes.