An online boutique is having a special on personalized baby items. On Monday, they sold 21 personalized baby blankets and 25 personalized hooded towels, for a total of $1,009 in receipts. The following day, they received orders for 4 personalized baby blankets and 17 personalized hooded towels, which brought in a total of $388. How much does each item sell for?
Let's assume the price of a personalized baby blanket is B and the price of a personalized hooded towel is H.
From the information given, we can write two equations:
21B + 25H = 1009 .....(1)
4B + 17H = 388 .....(2)
Multiplying equation (2) by 5, we get:
20B + 85H = 1940 .....(3)
Subtracting equation (1) from equation (3), we get:
20B + 85H - 21B - 25H = 1940 - 1009
-1B + 60H = 931 .....(4)
Substituting equation (4) into equation (2), we get:
4(-1B + 60H) + 17H = 388
-4B + 240H + 17H = 388
-4B + 257H = 388 .....(5)
Multiplying equation (5) by 20, we get:
-80B + 5140H = 7760 .....(6)
Adding equation (3) to equation (6), we get:
-80B + 5140H + 20B + 85H = 7760 + 1940
-60B + 5225H = 9700 .....(7)
Solving equations (4) and (7), we get:
B = (5225*931 - 60*9700)/(5225*-1-60) = 28
Substituting B = 28 into equation (1), we get:
21*28 + 25H = 1009
588 + 25H = 1009
25H = 421
H = 421/25 = 16.84
So each personalized baby blanket sells for $28 and each personalized hooded towel sells for $16.84. Answer: \boxed{28, 16.84}.