Alan, Terry and Mike have some marbles. Alan has 4 times as many marbles as Mike. Mike has 2/3 of the number of marbles Terry has. If Terry has 55 fewer marbles than Alan, how many marbles does each of them have?
a = 4m
m = 2/3 t
t = a-55
now solve as usual.
22 -> Mike
33 -> Terry
88 -> Alan
To solve this problem, let's assign variables to represent the number of marbles each person has.
Let's say Mike has x marbles.
According to the problem, Alan has 4 times as many marbles as Mike. So Alan has 4x marbles.
The problem also states that Mike has 2/3 of the number of marbles Terry has. Let's say Terry has y marbles. Therefore, Mike has 2/3y marbles.
Finally, the problem mentions that Terry has 55 fewer marbles than Alan. This means that Terry has 4x - 55 marbles.
Now we can set up equations based on the information given:
Alan: 4x marbles
Mike: x marbles
Terry: 4x - 55 marbles
We also know that:
Mike: 2/3y marbles
Now we can set up an equation based on Mike's and Terry's marbles:
2/3y = x
Now we can solve the equations to find the values of x, y, and 4x.
Substituting x = 2/3y into the equation 4x = 4(2/3y), we have:
4x = 8/3y
Multiplying both sides of the equation by 3/8 to solve for y:
y = (3/8)(8/3y)
y = y
This means y can have any value since y = y is always true. However, the problem does not state a specific value for y, so we cannot determine its exact value.
However, we can still find the value of x. Since x = 2/3y, we can substitute y with any value, such as 3, to find x:
x = 2/3(3)
x = 2
So Mike has 2 marbles.
Using this information, we can find the number of marbles Alan and Terry have:
Alan = 4x = 4(2) = 8 marbles
Terry = 4x - 55 = 4(2) - 55 = -47 marbles (This negative value suggests that our assumption for y = 3 was incorrect, as Terry cannot have a negative number of marbles.)
In conclusion:
Mike has 2 marbles.
Alan has 8 marbles.
Terry has -47 marbles (an invalid result).