Question

Gary found 72 shells and 40 coins at the beach. He wants to give them to some of his friends. Each friend will receive the same number of shells and the same number of coins. What is the greatest number of friends Gary can give shells and coins to? How many shells will each friend receive? How many coins? The greatest number of friends Gary can give shells and coins to is ____ friends. Each friend will receive__shells and __ coins

Answer 1

Let's begin by listing out the information given to us:

Gary found: 72 shells, 40 coins

To calculate for the greatest number of friends Gary can give shells and coins to, we will solve for the highrdt vommon factor (HCF)

`\begin{gathered} 72\Rightarrow2\cdot2\cdot2\cdot2\cdot3\cdot3 \\ 40\Rightarrow2\cdot2\cdot2\cdot5 \\ \therefore HCF=2\cdot2\cdot2=8 \end{gathered}`

The greatest number of friends Gary can give shells and coins to is 8

Each of the 8 friends receive:

`\begin{gathered} shells\colon(72)/(8)=9 \\ coins\colon(40)/(8)=5 \\ \therefore\text{They each receive 9 shells and 5 coins} \end{gathered}`

The greatest number of friends Gary can give shells and coins to is 8 friends. Each friend will receive 9 shells and 5 coins