the student store sells schools supplies,hats,and t-shirts with NAMS printed on them.The person who counted the hats and t-shirts can't remember exactly how many of each there were but he does remeber these 2 facts:

-there were four times as many t-shirts as hats
-there were 54 more t-shirts than hats.
How many t-shirts and hats were in the store.

t= 4h

t-h =54

sub the first into the second and solve

Let's solve this step-by-step.

Let's assume the number of hats is represented by 'H' and the number of t-shirts is represented by 'T'.

From the given information:
1. "There were four times as many t-shirts as hats." can be expressed as T = 4H.
2. "There were 54 more t-shirts than hats." can be expressed as T = H + 54.

Now, we have two equations:
T = 4H (equation 1)
T = H + 54 (equation 2)

We can substitute equation 1 into equation 2:
4H = H + 54

Let's solve for H:

4H - H = 54
3H = 54
H = 54 / 3 = 18

Now, let's substitute the value of H (18) into equation 1 to find T:

T = 4H
T = 4 * 18
T = 72

Therefore, there are 18 hats and 72 t-shirts in the store.

To solve this problem, we can use algebraic equations to represent the information provided. Let's assign variables to the number of hats and t-shirts.

Let's say:
H = Number of hats
T = Number of t-shirts

From the given information, we have two facts:
1. "There were four times as many t-shirts as hats" means T = 4H.
2. "There were 54 more t-shirts than hats" means T = H + 54.

Now, we can solve these two equations simultaneously to find the values of H and T.

Substitute the value of T from the second equation into the first equation:
H + 54 = 4H

Rearrange the equation:
4H - H = 54

Combine like terms:
3H = 54

Divide both sides by 3:
H = 18

Substitute the value of H in either equation to find T:
T = H + 54 = 18 + 54 = 72

Therefore, there were 18 hats and 72 t-shirts in the store.