Gerry has a total of 30 pens and pencils. He decided to trade with his friends all his pens for pencils. If he traded every pen for 2 pencils he would have 48pencils in all. How many pens and how many pencils did he have before the trade
Let's say Gerry had X pens and Y pencils before the trade.
We know that the total number of pens and pencils Gerry had is 30, so we can write the equation X + Y = 30. (Equation 1)
We also know that if he traded every pen for 2 pencils, he would have 48 pencils in all. This means that the number of pencils he got from trading all his pens is 2X. So we can write the equation Y + 2X = 48. (Equation 2)
We can now solve this system of equations.
Let's multiply Equation 1 by 2 in order to cancel out the X terms when we combine it with Equation 2.
2X + 2Y = 60. (Equation 3)
Combining Equation 3 with Equation 2, we have:
(2X + 2Y) - (Y + 2X) = 60 - 48
2X + 2Y - Y - 2X = 12
X + Y = 12. (Equation 4)
Now we have a new equation that we can use to solve for X and Y.
We can subtract Equation 4 from Equation 1:
(X + Y) - (X + Y) = 30 - 12
0 = 18
This means that Equation 1 and Equation 4 are not compatible, and there is no consistent answer to this problem.
Therefore, we cannot determine how many pens and how many pencils Gerry had before the trade based on the given information.
Let's solve this step by step.
Let's assume that Gerry had x number of pens before the trade.
So, before the trade, Gerry had x pens and (30 - x) pencils.
If Gerry traded every pen for 2 pencils, he would have 2 * x pencils.
According to the given information, 2 * x pencils should be equal to 48 pencils.
This can be written as the equation: 2x = 48.
To find the value of x, we can solve this equation.
Dividing both sides of the equation by 2, we get: x = 24.
So, Gerry had 24 pens (x) and 6 pencils (30 - x) before the trade.