Show work please

Question

Sarah and genesis are making bracelets. It takes 2 hours to make a small bracelet and 3 hours to make a large bracelet . they have 24 hours to make 10 bracelets. A small.bracelet costs 8$ and a large bracelet  costs 10$. What's the MOST amount of money they can bring in. (88 is not the answer)

Answer 1

S + L = 10  -->  S = 10 - L

2S + 3L = 24

2(10 - L) + 3L = 24

20 - 2L + 3L = 24

20 + L = 24

L = 24 - 20 = 4

 

S = 10 - L = 10 - 4  = 6

 

$8S *$10L = $8*6 + $10*4 = $88

 

 

Since the answer is not $88, let's try a different method.

 

If they make all large bracelets, they can make 24/3=8 bracelets in that time, bringing in $10*8=$80, which is even less.

 

If they make all small bracelets, they can make 24/2=12 bracelets in that time, bringing in $8*12=$96, which is even more. This would be the most profitable strategy would to be making $8 every two hours on small bracelets (or $4 an hour) rather than wasting their time making $10 every three hours on large bracelets (or $3.33 an hour). However, if they can only make 10 bracelets, they would only make $8*10=$80, which is less again.

 

If the answer is not $88 and can't be $96, the only other thing I can think of is maybe doubling their output in that time since there are two girls making bracelets.