The Brady family received 1 letter on July 28.
Step-by-step explanation:
Step 1:
Assume a = the number of letters, b = the number of bills, c = the number of ads, and d = the number of magazines.
From the question, they got 15 pieces of mail that day so [tex]a+b+c+d=15.[/tex]
They got 5 more magazines than bills so [tex]d = b + 5.[/tex]
The got the same number of letters as ads so [tex]a=c.[/tex]
They got 3 more bills than ads so [tex]b= c + 3.[/tex]
Step 2:
As we have only one equation to solve the values, we need to make every term in terms of a single term.
We make everything in terms of c.
So [tex]a=c, b = c+3, c=c, d = b+5 = (c+3)+5=c+8.[/tex]
Substituting all this in the equation, we get
[tex]a + b+c+d =(c)+(c+3)+(c)+(c+8) = 15, 4c+11=15.[/tex]
[tex]4c=4, c = 1.[/tex]
Step 3:
Substituting c = 1 in other terms, we get
[tex]a=c=1,[/tex]
[tex]b=c+3=1+3=4,[/tex]
[tex]c=1,[/tex] and
[tex]d = c+8 = 1+8=9.[/tex]
As a = 1, they received 1 letter that day.
