Answer:
The initial amount of cupcakes = 48
If they sold each cupcake for $2.75, they would make $132 which is more than the required $100 to go on band field trip to New York.
The excess money available for spending is thus $32
Step-by-step explanation:
The complete question is presented in the attached image to this answer.
They need to make $100
Let x be the initial amount of cupcakes
During the first hour, Brady sold (1/3) of the cupcakes and Jaquan sold (3/8)
Total amount of cupcakes sold in the first hour = [(1/3) × x] + [(3/8) × x] = (17x/24)
Amount of cupcakes remaining after the first hour = x - (17x/24) = (7x/24)
After the first hour, they sold 2 cupcakes
Amount of cupcakes left after the first hour = (7x/24) - 2 = (0.292x - 2)
During the second hour, they sold 75% of the remaining cupcakes, meaning they had 25% of the remaining cupcakes left.
Amount of cupcakes left = 25% × (0.292x - 2)
= (0.07292x - 0.5)
During the third hour, they sold the remaining 3 cupcakes
Meaning that the amount of cupcakes left from the second hour = 3
(0.07292x - 0.5) = 3
0.07292x = 3.5
x = (3.5/0.07292) = 47.998 = 48 cupcakes.
Hence, the initial amount of cupcakes = 48.
If they sold each cupcake for $2.75, they would make 2.75 × 48 = $132
Which is more than the required $100 to go on band field trip to New York.
The excess money available for spending is thus $132 - $100 = $32.
Hope this Helps!!!
