in her coin collection, holly has 1/3 more coins than jim has in his collection. if the number of coins in 1/2 of holly's collection is 10 more than the number of coins in 1/3 of jim's collection, how many coins does each have?
To find out how many coins Holly and Jim have, we'll break down the problem into smaller steps.
Let's assume Jim has x number of coins in his collection.
According to the problem, Holly has 1/3 more coins than Jim. Therefore, Holly has x + (1/3)x = (4/3)x coins in her collection.
The problem also states that the number of coins in 1/2 of Holly's collection is 10 more than the number of coins in 1/3 of Jim's collection.
1/2 of Holly's collection is (1/2)((4/3)x) = (2/3)x.
1/3 of Jim's collection is (1/3)x.
So, we can now create the equation: (2/3)x = (1/3)x + 10.
To solve this equation:
Move (1/3)x from the right side to the left side: (2/3)x - (1/3)x = 10.
Simplify the left side: (1/3)x = 10.
Multiply both sides by 3 to isolate x: 3 * (1/3)x = 3 * 10.
Simplify: x = 30.
Now that we know x (Jim's number of coins), we can find Holly's number of coins:
Holly has (4/3)x = (4/3)(30) = 40 coins.
Therefore, Jim has 30 coins and Holly has 40 coins.