Answer:
The total number of nails in Susan's box is 660 nails
Step-by-step explanation:
The given parameters are;
The number of small nails in John's box = 65
The number of medium nails in John's box = 40
The number of large nails in John's box = 45
The number of medium nails in Susan's box = 176
The ratio of the nails in John's box is given as follows;
The ratio of small nails in John's box = 65/(65 + 40 + 45) = 13/30
The ratio of medium nails in John's box = 40/(65 + 40 + 45) = 4/15 = 8/30
The ratio of large nails in John's box = 45/(65 + 40 + 45) = 3/10 = 9/30
Given that the proportion of the nails in John's box and Susan's box are the same, we have;
The ratio of medium nails in Susan's box = 8/30
Therefore;
Where the total number of nails in Susan's box = X, we have;
8/30 × X = 176
X = 176 × 30/8 = 660 nails
The total number of nails in Susan's box = 660 nails.
