The ratio of Tim's marbles to Joe's marbles to Matt's marbles is 8 : 6 : 9. If Tim and Joe have 84 marbles altogether, how many marbles does Matt have?
Show your work please?
84/14 = 6
Tim: 48
Joe: 36
Matt: 54
To find out how many marbles Matt has, we first need to determine the ratio between the number of marbles that Tim and Joe have. The given ratio is 8:6, which means that for every 8 marbles Tim has, Joe has 6 marbles.
To calculate the actual number of marbles for Tim and Joe, we need to set up a proportion. Let the number of marbles Tim has be represented by 'x' and the number of marbles Joe has be represented by 'y'.
We can set up the following proportion based on the given ratio:
8 / 6 = x / y
To solve for 'x' and 'y', we can cross-multiply and then solve for 'y':
8y = 6x
Now, we know that Tim and Joe have 84 marbles altogether. So, we can form another equation using this information:
x + y = 84
We can substitute 8y for 6x in the second equation to solve for 'y':
8y + y = 84
9y = 84
y = 84 / 9
y = 9.33
However, the number of marbles must be a whole number, so we round down y to the nearest whole number since we cannot have fractional marbles.
Therefore, Joe has 9 marbles.
Now that we know the number of marbles for Joe, we can plug that value into the original equation for Tim and Joe:
8 / 6 = x / 9
48 = 6x
x = 48 / 6
x = 8
So, Tim has 8 marbles.
Finally, to find out how many marbles Matt has, we add up the marbles for Tim, Joe, and Matt:
8 + 9 + z = Total number of marbles
Since we are given that the ratio of Tim's marbles to Joe's marbles to Matt's marbles is 8:6:9, we can express the number of marbles Matt has as 9z, where 'z' represents a constant.
Now, we can solve for 'z':
8 + 9 + 9z = Total number of marbles
17 + 9z = Total number of marbles
However, we do not have enough information to calculate the total number of marbles or the actual number of marbles Matt has.