first off let's establish what's happening here. Emma has brought two bottles of shampoo which is assumed to have the exact same amount of shampoo in them initially. She used 3/8 of the volume of shampoo of the first bottle and used 7/10 of the remaining shampoo which I am assuming is the second bottle of shampoo since Emma initially brought two bottles of shampoo. Since the question is asking for the remaining amount of shampoo it seems that both fractions 3/8 and 7/10 need to be added to find the remaining amount of shampoo which the denominator representing the total amount of shampoo in both bottles at the start of this problem.
so this can be set up 3/8+7/10 since eighths are greater than tenths as fractions.
find the common denominator must e found by multiplying 7/10 by 8 and 3/8 by 10 for the numerator and denominator for both fractions. Then we get this
30/80+56/80=86/80. assuming she only used the first bottle then 86/80 is the answer which shows she used the whole bottle.