A magician has 3 more red hats than black hats and 4 fewer purple hats than black hats and has 14 hatsin all. How many hats of each color does he have. Show how you got the answer.

You can get the answer by using algebra or by guessing the number of black and seeing what works.

Perhaps you are not learning algebra yet.

If I guess there are 5 black hats, then there are 8 red ones and 1 purple one. The sum is 14. So that's the answer.

B+3=R

B-4=P

B+P+R=14

substitute for P and R

(B)+(B-4)+(B+3)=14

3B-1=14

solve from here

To solve this problem, let's represent the number of black hats as x.

According to the given information, the magician has 3 more red hats than black hats. So, the number of red hats would be x + 3.

Similarly, the magician has 4 fewer purple hats than black hats. Hence, the number of purple hats would be x - 4.

We are also given that the magician has a total of 14 hats. So, we can write the equation:

x + (x + 3) + (x - 4) = 14

Now, let's solve the equation by combining like terms:

3x - 1 = 14

Next, isolate x by adding 1 to both sides of the equation:

3x = 15

Finally, divide both sides of the equation by 3 to solve for x:

x = 5

Therefore, the magician has 5 black hats.

To find the number of red hats, we substitute x back into the expression x + 3:

5 + 3 = 8

So, the magician has 8 red hats.

To find the number of purple hats, we substitute x back into the expression x - 4:

5 - 4 = 1

Therefore, the magician has 1 purple hat.

In summary, the magician has 5 black hats, 8 red hats, and 1 purple hat.