Question

Alec, Ben, and Cedric collect coins. Alec says he has 5 less than 1 2/3 times the number of coins Ben has. Cedric says he has 12 more than 1 1/2 times the number of coins Ben has. If Alec and Cedric have the same number of coins, how many coins does Ben have? How many coins do Alec and Cedric each have?

Answer 1

Ben has 102 coins. Alec has 170 coins and Cedric has 168 coins.

Step-by-step explanation:

Let's start by assigning variables to the number of coins each person has:

Let's say Ben has x coins.

Alec says he has 5 less than 1 2/3 times the number of coins Ben has. This can be represented as:

Alex = 1 2/3x - 5

Cedric says he has 12 more than 1 1/2 times the number of coins Ben has. This can be represented as:

Cedric = 1 1/2x + 12

We also know that Alec and Cedric have the same number of coins:

Alex = Cedric

Now we can set up an equation:

1 2/3x - 5 = 1 1/2x + 12

To solve this equation, we can multiply both sides by 6 to get rid of the fractions:

6(1 2/3x - 5) = 6(1 1/2x + 12)

10x - 30 = 9x + 72

Subtract 9x from both sides:

x - 30 = 72

Add 30 to both sides:

x = 102

So Ben has 102 coins.

Now we can substitute x = 102 into our equations to find the number of coins Alec and Cedric have:

Alec = 1 2/3(102) - 5 = 170

Cedric = 1 1/2(102) + 12 = 168