# Children's 6140

The store received a total of 666 pairs of children's, men's and women's shoes. Men were 2.5 times less than children, while children were 1.4 times more than women. Express in whole numbers the ratio of the number of pairs of children's, men's, and women's shoes. How many were there?

a =  315
b =  126
c =  225
p = 35:14:25

## Step-by-step explanation:

a+b+c = 666
b = a/2.5
a = 1.4 · c

a+b+c = 666
0.4a-b = 0
a-1.4c = 0

Row 2 - 0.4 · Row 1 → Row 2
a+b+c = 666
-1.4b-0.4c = -266.4
a-1.4c = 0

Row 3 - Row 1 → Row 3
a+b+c = 666
-1.4b-0.4c = -266.4
-b-2.4c = -666

Row 3 - -1/-1.4 · Row 2 → Row 3
a+b+c = 666
-1.4b-0.4c = -266.4
-2.114c = -475.714

c = -475.71428571/-2.11428571 = 225
b = -266.4+0.4c/-1.4 = -266.4+0.4 · 225/-1.4 = 126
a = 666-b-c = 666-126-225 = 315

a = 315
b = 126
c = 225

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