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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.
Using proportions, it is found that the total number of nails in Susan's box was 660.
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- John had 65 + 40 + 45 = 150 nails.
- The proportion of medium nails is: [tex]\frac{40}{150}[/tex]
- Susan's box has x nails.
- Of those nails, 176 are medium. Thus, the proportion of medium nails out of the total in Susan's box is of: [tex]\frac[176}{x}[/tex]
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Since the proportions are equal:
[tex]\frac{40}{150} = \frac{176}{x}[/tex]
[tex]40x = 150\times176[/tex]
[tex]x = \frac{150\times176}{40}[/tex]
[tex]x = 660[/tex]
The total number of nails in Susan's box was 660.
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