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 johns box. There are 176 medium nails in susan's box. What is the total number of nails in susan's box?

Answer 1

Answer:

medium nails in John = 40

medium nails in susan = 176

40/176

=5/22

so proportion is 5:22

Answer 2

In Susan's box, there is a total of 642 nails.

Given:

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 johns box. There are 176 medium nails in Susan's box.

To Find:

The total number of nails in Susan's box.

Solution:

It is given that Susan has a box of nails that has the same proportion of small, medium, and large nails as johns box, so, find the proportion of small nails, medium nails, and large nails.

${\rm small:medium:large}=65:40:45\\=13:8:9$

This proportion is the same for the nails that Susan has. Also, Susan has 176 medium nails.

Let the number of small nails, medium nails, and large nails are

13x, 8x, and 9x.

As, 8x=176.

So, x=22

Substitute x=22 in 13x, 8x, and 9x and find the number of respective nails that Susan has.

$13\times 22=268\\8\times 22=176\\9\times 22=198$

Add 268, 176, and 198.

268+176+198=642

Thus, in Susan's box, there is a total of 642 nails.

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