Answer:
They baked 108 cookies
Step-by-step explanation:
Assume that Jada and Diego baked x cookies
∵ Jada and Diego baked x cookies
∵ They select [tex]\frac{1}{4}[/tex] of the cookies to give to their teachers
∴ They give their teachers = [tex]\frac{1}{4}[/tex] × x = [tex]\frac{1}{4}[/tex] x
- Find the remaining cookies
∴ The remaining cookies = x - [tex]\frac{1}{4}[/tex] x = [tex]\frac{3}{4}[/tex] x
∵ They threw away one burnt cookie
∴ The remaining cookies = [tex]\frac{3}{4}[/tex] x - 1
∵ They delivered [tex]\frac{2}{5}[/tex] of the remaining cookies to a local nursing home
- That means the new remaining will be [tex]\frac{3}{5}[/tex] of the old remaining
∴ The new remaining = [tex]\frac{3}{5}[/tex] ( [tex]\frac{3}{4}[/tex] x - 1) = [tex]\frac{9}{20}[/tex] x - [tex]\frac{3}{5}[/tex]
∵ They gave 3 cookies to some neighborhood kids
∴ The next remaining = [tex]\frac{9}{20}[/tex] x - [tex]\frac{3}{5}[/tex] - 3
- Add the like terms
∴ The next remaining = [tex]\frac{9}{20}[/tex] x - [tex]\frac{18}{5}[/tex]
∵ They wrapped up [tex]\frac{2}{3}[/tex] of the remaining cookies to save for their friends
- That means the last remaining will be [tex]\frac{1}{3}[/tex] of the previous remaining
∴ The last remaining = [tex]\frac{1}{3}[/tex] ( [tex]\frac{9}{20}[/tex] x - [tex]\frac{18}{5}[/tex] )
∴ The last remaining = [tex]\frac{3}{20}[/tex] x - [tex]\frac{6}{5}[/tex]
∵ They had 15 cookies left
- Equate the last remaining by 15 to find x
∴ [tex]\frac{3}{20}[/tex] x - [tex]\frac{6}{5}[/tex] = 15
- Add [tex]\frac{6}{5}[/tex] to both terms
∴ [tex]\frac{3}{20}[/tex] x = [tex]\frac{81}{5}[/tex]
- Divide both sides by [tex]\frac{3}{20}[/tex]
∴ x = 108
They baked 108 cookies
