Maggie bought freight trains for her model train set. She spent $99 on them. Gage bought some model trains too. He spent $66 on them. Each train costs the same amount. At most, how much could each model freight train cost?
At most, a model freight train could cost how much?
66 = 2/3 of 99
To find out the maximum cost of each model freight train, we need to divide the total amount spent by the number of trains bought.
Maggie spent $99 on freight trains, and Gage spent $66 on model trains.
Let's assume both of them bought the same number of trains.
If x represents the cost of each train, then:
Maggie bought $99/x trains, and Gage bought $66/x trains.
The total number of trains bought is given by:
$99/x + $66/x.
To find the maximum cost of each model freight train, we want to maximize the value of x. This means we want to minimize the total number of trains bought.
To minimize $99/x + $66/x, we need to find the least common multiple (LCM) of 99 and 66. The LCM of 99 and 66 is 198. Therefore, the maximum cost of each model freight train is $99/198, which is equal to $0.50.
Therefore, at most, each model freight train could cost $0.50.
To find out the maximum price that each model freight train could cost, we divide the total amount spent by the number of trains bought.
Maggie spent $99 on freight trains and Gage spent $66. Since each train costs the same amount, the total number of trains bought by both of them is the same.
We can find the cost of each train by dividing the total amount spent by the number of trains bought. So, we divide $99 by the number of trains Maggie bought, and $66 by the number of trains Gage bought.
Let's assume Maggie bought x number of trains. So, the cost of each train would be $99 divided by x.
And let's assume Gage bought y number of trains. So, the cost of each train for Gage would be $66 divided by y.
Since both Maggie and Gage bought the same number of trains, we can set x=y.
Therefore, the cost of each train could be at most the minimum of ($99/x, $66/x).
To find the maximum value, we need to find the minimum value of x that makes the cost of each train as high as possible.
Since we are looking for the maximum value, we need to find the minimum of $99/x and $66/x. Thus, the maximum cost for each train would be the smallest of these two fractions.
To determine the maximum cost, we need to compare these two fractions and find the minimum.
number of models bought by Maggie ---- x
cost of each = 99/x
number of models bought by Gage ---- y
cost of each = 66/y
99/x = 66/y
3/x = 2/y
2x = 3y
x = 3y/2 , but x must be a whole number, so 3y/2 must be a whole number
the smallest such number is when y = 2, then x = 3
or , let y = 6, then x = 9
let y = 40, then x = 60
Of course the highest cost of a model would be when the x and y are the lowest numbers, which would be 99/3 = $33.00