Gerry had a total of 30 pens and pencils. He decided to trade with his friends all of his pens and pencils. If he traded every pen for 2 pencils, he would have 48 pencils in all. How many pens and how many pencils did he have before the trade?
Let p = pens
Pencils = 30-p
Total pencils after the exchange will be: 48 = 30-p + 2p
48 = 30 + p
18 = p (pens)
30-18 = 12 pencils
To check: 18×2 + 12 = 36+12 = 48
Well, it seems Gerry experienced a classic case of "pencilflation"! Let's do some math and solve this puzzle.
Let's assume Gerry had P pens and P pencils before the trade. After trading, he had 2P pencils, as each pen got swapped for 2 pencils.
According to the problem, he had a total of 30 pens and pencils to begin with. So we can write the equation:
P + P = 30
Simplifying it:
2P = 30
Now, we know that after the trade he had 48 pencils, which is 2P. So we can write another equation:
2P = 48
Let's solve this equation to find the value of P and determine the number of pens and pencils Gerry had before the trade.
Dividing both sides of the equation by 2:
P = 48/2
P = 24
So Gerry had 24 pens and 24 pencils before the trade.
Just remember, next time Gerry decides to trade, he should probably double-check his pencilconomics!
Let's assume Gerry had x pens before the trade. Since he traded every pen for 2 pencils, he had 2x pencils after the trade.
We know that Gerry had a total of 30 pens and pencils, so we can write the equation:
x + 2x = 30
Combining like terms, we get:
3x = 30
To solve for x, we divide both sides of the equation by 3:
x = 30 / 3
x = 10
So, Gerry had 10 pens before the trade.
Now, to find the number of pencils he had before the trade, we substitute the value of x into the equation:
2x = 2 * 10
2x = 20
Therefore, Gerry had 10 pens and 20 pencils before the trade.
To solve this problem, we can set up a system of equations. Let's represent the number of pens that Gerry had initially as 'x', and the number of pencils as 'y'.
We are given two pieces of information:
1) Gerry had a total of 30 pens and pencils: x + y = 30
2) If he traded every pen for 2 pencils, he would have 48 pencils in all: y = 2x + 48
We can now solve this system of equations to find the values of 'x' and 'y'.
Substituting the value of 'y' from the second equation into the first equation:
x + (2x + 48) = 30
3x + 48 = 30
3x = 30 - 48
3x = -18
x = -18/3
x = -6
Now, substituting the value of 'x' back into the second equation:
y = 2(-6) + 48
y = -12 + 48
y = 36
Therefore, Gerry had -6 pens and 36 pencils before the trade.