Answer
Cost of one t-shirt = $12.5
Cost of one tank top = $6.99
Step-by-step explanation
Let the cost of one T-shirt be x
Let the cost of one tank top be y
Laura purchased 3 t-shirts and 5 tank tops for $72.45
3x + 5y = 72.45
Trisha bought 4 t-shirts and 3 tank tops for $70.97
4x + 3y = 70.97
Now we have simultaneous equations
3x + 5y = 72.45
4x + 3y = 70.97
To solve this, we will use the elimination method.
Trying to eliminate y first, we multiply eqn 1 by 3 and 5
(3x + 5y = 72.45) × 3
(4x + 3y = 70.97) × 5
9x + 15y = 217.35
20x + 15y = 354.85
Subtract eqn 1 from eqn 2
20x - 9x + 15y - 15y = 354.85 - 217.35
11x = 137.5
Divide both sides by 11
(11x/11) = (137.5/11)
x = 12.5
We can then solve for y using either of the two original equations
3x + 5y = 72.45
Recall, x = 12.5
3(12.5) 5y = 72.45
37.5 + 5y = 72.45
Subtract 37.5 from both sides
5y = 72.45 - 37.5
5y = 34.95
Divide both sides by 5
(5y/5) = (34.95/5)
y = 6.99
Solving this simultaneously, we obtain that
x = 12.5
y = 6.99
Hope this Helps!!!