Gene ad jay has collection of marbles. If jay give gene 2 of his marbles they would have an equal number. But if gene give jay 2 marbles, jay have 2 times as many as gene. How many marblea does jay have?
put all those words into math:
j-2 = g+2
j+2 = 2(g-2)
Now just solve for j
Gene 10 Jay 14
To solve this problem, let's assign variables to the number of marbles Gene and Jay initially have. Let's say Gene has G marbles, and Jay has J marbles.
According to the problem statement, if Jay gives Gene 2 marbles, they would have an equal number. This can be represented by the equation:
J - 2 = G + 2
Similarly, if Gene gives Jay 2 marbles, Jay would have twice as many marbles as Gene:
J + 2 = 2(G - 2)
Now we have a system of two equations. We can solve them to find the value of J, the number of marbles Jay has.
Let's solve equation 1 for G:
G = J - 4
Substituting this value of G into equation 2, we get:
J + 2 = 2(J - 4 - 2)
J + 2 = 2J - 12
12 + 2 = 2J - J
14 = J
Therefore, Jay has 14 marbles.
To validate this answer, let's check it using the given conditions:
- If Jay gives Gene 2 marbles, Jay will have 14 - 2 = 12 marbles, and Gene will have 4 marbles. (12 - 2 = 4 + 2) This matches the given condition.
- If Gene gives Jay 2 marbles, Jay will have 14 + 2 = 16 marbles, and Gene will have 2 marbles. (16 - 2 ≠ 2 * (2 - 2)) This condition does not match.
Hence, the answer is that Jay has 14 marbles.