Alicia and Lewis have 99 total coins. Lewis' collection has 2 times as many coins in it as Alicia's collection. How many coins are in Lewis' collection? How many coins are in Alicia's collection?
21
To find the number of coins in Alicia's collection and Lewis' collection, we can set up a system of equations based on the given information.
Let's say the number of coins in Alicia's collection is "a", and the number of coins in Lewis' collection is "l".
From the problem statement, we can derive two equations:
1) Alicia and Lewis have a total of 99 coins:
a + l = 99
2) Lewis' collection has 2 times as many coins as Alicia's collection:
l = 2a
To solve this system of equations, we can use the substitution method. Rearrange equation 2 to solve for "a" in terms of "l":
a = l/2
Substitute this value of "a" into equation 1:
l/2 + l = 99
Combine like terms:
3l/2 = 99
To solve for "l", multiply both sides of the equation by 2/3:
l = (2/3) * 99
l = 66
Therefore, Lewis has 66 coins in his collection.
To find Alicia's collection, substitute the value of "l" back into equation 2:
66 = 2a
Divide both sides by 2:
a = 33
Therefore, Alicia has 33 coins in her collection.
2c + c = 99
Solve for c to find the number in Alicia's collection.