document.write( "Question 838940: a famer employs two students to pack peaches into trays for a market. at the end of the day they have packed a total of 288 trays. if student A packed 5 trays for every 7 that student B packed how many did each of them pack (show working) \n" ); document.write( "
Algebra.Com's Answer #505448 by Theo(13342)\"\" \"About 
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x = number of trays that student A packed.
\n" ); document.write( "y = number of trays that student B packed.
\n" ); document.write( "together they packed 288 trays, so you get:
\n" ); document.write( "x + y = 288
\n" ); document.write( "student A packed 5 trays for every 7 that student B packed.
\n" ); document.write( "you get the ratio:
\n" ); document.write( "x/y = 5/7
\n" ); document.write( "multiply both sides of this equation by y to get:
\n" ); document.write( "x = 5/7 * y
\n" ); document.write( "you have 2 equations that need to be solved simultaneously.
\n" ); document.write( "they are:
\n" ); document.write( "x + y = 288
\n" ); document.write( "x = 5/7 * y
\n" ); document.write( "you can substitute 5/7 * y for x in the first equation to get:
\n" ); document.write( "x + y = 288 becomes:
\n" ); document.write( "5/7 * y + y = 288
\n" ); document.write( "multiply the second y by 7/7 to get 7/7 * y which is equivalent to y.
\n" ); document.write( "your equation becomes:
\n" ); document.write( "5/7 * y + 7/7 * y = 288
\n" ); document.write( "factor out the y to get:
\n" ); document.write( "(5/7 + 7/7) * y = 288
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "12/7 * y = 288
\n" ); document.write( "multiply both sides of this equation by 7/12 to get:
\n" ); document.write( "y = 288 * 7 / 12
\n" ); document.write( "simplify to get:
\n" ); document.write( "y = 168
\n" ); document.write( "substitute for y in the first equation of x + y = 288 to get:
\n" ); document.write( "x = 120
\n" ); document.write( "your solution is:
\n" ); document.write( "x = 120 and y = 168
\n" ); document.write( "replace x and y in the original equations to confirm the answer is good.
\n" ); document.write( "x + y = 288 becomes 120 + 168 = 288 which becomes 288 = 288 which is true.
\n" ); document.write( "x/y = 5/7 becomes 120 / 168 = 5/7
\n" ); document.write( "simplify 120 / 168 by dividing numerator and denominator by 24 to get:
\n" ); document.write( "5/7 = 5/7 which is true.
\n" ); document.write( "x = 120 and y = 168 have been confirmed as good solutions so you're done.
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