Question

John has a box of nails. The box contains 65 small nails, 40 medium nails, and 45 large nails. Susan has a box of nails that has the same proportion of small, medium, and large nails as John's box. There are 176 medium nails in Susan's box. What is the total number of nails in Susan's box? ​

Answer 1

The total number of nails in Susan's box is 660 nails

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.