document.write( "Question 802717: The oldest child in a family is 5 years older than her brother. The mother is 1 year younger than twice the sum of her kid's ages. The father's age equals the mother's age plus the son's age. If the sum of all 4 ages is three times a prime number and the mom was younger than 50 when she had her 2nd child how old is the daughter? \n" ); document.write( "
Algebra.Com's Answer #484103 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
let d = age of the daughter
\n" ); document.write( "let b = age of the brother
\n" ); document.write( "let m = age of the mother
\n" ); document.write( "let f = age of the father
\n" ); document.write( "let p = prime number referred to in the problem
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement
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\n" ); document.write( "The oldest child in a family is 5 years older than her brother.
\n" ); document.write( "d = b + 5
\n" ); document.write( ":
\n" ); document.write( " The mother is 1 year younger than twice the sum of her kid's ages.
\n" ); document.write( "m = 2(d+b) - 1
\n" ); document.write( "m = 2d + 2b - 1
\n" ); document.write( ":
\n" ); document.write( " The father's age equals the mother's age plus the son's age.
\n" ); document.write( "f = m + b
\n" ); document.write( ":
\n" ); document.write( " If the sum of all 4 ages is three times a prime number
\n" ); document.write( "d + b + m + f = 3p
\n" ); document.write( "replace m with (2d+2b-1)
\n" ); document.write( "d + b + (2d+2b-1) + f = 3p
\n" ); document.write( "3d + 3b + f = 3p+1
\n" ); document.write( "Replace f with (m+b)
\n" ); document.write( "3d + 3b + (m+b) = 3p+1
\n" ); document.write( "3d + 4b + m = 3p+1
\n" ); document.write( "replace m with (2d+2b-1) again
\n" ); document.write( "3d + 4b + (2d+2b-1) = 3p+1
\n" ); document.write( "5d + 6b = 3p + 1 + 1
\n" ); document.write( "5d + 6b = 3p + 2
\n" ); document.write( "Replace d with (b+5)
\n" ); document.write( "5(b+5) + 6b = 3p + 2
\n" ); document.write( "5b + 25 + 6b = 3p + 2
\n" ); document.write( "11b = 3p + 2 - 25
\n" ); document.write( "11b = 3p - 23
\n" ); document.write( "rearrange to
\n" ); document.write( "3p = 11b + 23
\n" ); document.write( "divide by 3
\n" ); document.write( "p = \"11%2F3\"b + \"23%2F3\"
\n" ); document.write( "Find a value for b that makes p a prime number
\n" ); document.write( "when b = 8, (brother's age) and p = 37, sum of all 4 ages: 3*37 = 111
\n" ); document.write( "then
\n" ); document.write( "d = 8+5
\n" ); document.write( "d = 13 yrs, daughter's age
\n" ); document.write( "m = 2(8+13)) - 1
\n" ); document.write( "m = 41 yrs is Mom's age
\n" ); document.write( "f = 41 + 8
\n" ); document.write( "f = 49 yrs is Dad's age
\n" ); document.write( ":
\n" ); document.write( "See if that adds up 8 + 13 + 41 + 49 = 111
\n" ); document.write( ":
\n" ); document.write( "Sorry about the first attempt, got hung up on 5th grade math!\r
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