When 306 stamps were shared among Pat, Kyle, and Ryan, Pat got twice as many stamps as what Kyle and Ryan got together. If Kyle got 18 stamps more than Ryan, how many stamps did Ryan get? Don't forget to show your work.
Pat= x , Kyle= y, Ryan= z
x+y+z= 306
2x= y+z
z+18=y
So from here, you just plug the equations into each other...
2x= y+z
so, 2x= (z+18)+z
so, 2x= 2z+18
so, x= (2z+18) /2
Then you plug this in to the equation: x+y+z= 306
So... (2z+18) /2 + (z+18) + z = 306
Then, 4z+38 = 612
4z = 576
z or Ryan= 144 stamps
Let's solve this step-by-step:
Let's assume that the number of stamps Ryan got is 'x'.
Since Kyle got 18 stamps more than Ryan, Kyle got 'x + 18' stamps.
Pat got twice as many stamps as what Kyle and Ryan got together, so Pat got 2 * (x + x + 18) stamps.
The total number of stamps is 306, so we can equate the sum of the stamps each person got to 306:
x + x + 18 + 2 * (x + x + 18) = 306
Simplifying the equation:
2x + 18 + 4x + 36 = 306
Combining like terms:
6x + 54 = 306
Subtracting 54 from both sides:
6x = 252
Dividing both sides by 6:
x = 42
Therefore, Ryan got 42 stamps.
Let's break down the information given in the question:
1. Pat got twice as many stamps as what Kyle and Ryan got together.
2. Kyle got 18 stamps more than Ryan.
3. The total number of stamps is 306.
To solve this problem, we can set up a system of equations.
Let's represent the number of stamps Ryan got as "R".
According to the second piece of information, Kyle got 18 stamps more than Ryan, so we can write Kyle's number of stamps as "R + 18".
Lastly, Pat got twice as many stamps as what Kyle and Ryan got together, so we can write Pat's number of stamps as "2 * (R + R + 18)" or "4R + 36".
Now, let's set up the equation based on the total stamps:
R + (R + 18) + (4R + 36) = 306
Simplifying the equation, we have:
6R + 54 = 306
Now, let's isolate the variable "R" by subtracting 54 from both sides of the equation:
6R = 306 - 54
6R = 252
Finally, divide both sides of the equation by 6 to solve for "R":
R = 252 / 6
R = 42
Therefore, Ryan got 42 stamps.
To summarize:
- Ryan got 42 stamps.
- Kyle got 42 + 18 = 60 stamps.
- Pat got 2 * (42 + 60) = 204 stamps.
If you have any further questions, feel free to ask!