Question

Ruth has 2 bags of marbles and 4 loose marbles, as shown. Liam has 1 bag of marbles and 10 loose marbles, as shown. There are the same number of marbles in each bag. Ruth's Marbles (Suggested maximum time: 5 minutes) Ruth and Liam each have the same total number of marbles. Work out how many marbles are in each bag. Number of Marbles: Liam's Marbles ​

Answer 1

There are 6 marbles in each bag.

Explanation:

Let x be the number of marbles in each bag.

If Ruth has 2 bags of marbles and 4 loose marbles, the expression that models the total number of marbles that Ruth has is:

`2x + 4`

If Liam has 1 bag of marbles and 10 loose marbles, the expression that models the total number of marbles that Liam has is:

`x + 10`

We know that Ruth and Liam have the same total number of marbles, so we can equate the two expressions:

`\begin{aligned}\textsf{Total marbles for Ruth} &= \textsf{Total marbles for Liam}\\\\2x+4&=x+10\end{aligned}`

To find the number of marbles in each bag, we can solve the equation for x:

`\begin{aligned}2x+4&=x+10\\2x+4-x&=x+10-x\\x+4&=10\\x+4-4&=10-4\\x&=6\end{aligned}`

So, there are 6 marbles in each bag.