SOLUTION: 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 stud

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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)
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
x = number of trays that student A packed.
y = number of trays that student B packed.
together they packed 288 trays, so you get:
x + y = 288
student A packed 5 trays for every 7 that student B packed.
you get the ratio:
x/y = 5/7
multiply both sides of this equation by y to get:
x = 5/7 * y
you have 2 equations that need to be solved simultaneously.
they are:
x + y = 288
x = 5/7 * y
you can substitute 5/7 * y for x in the first equation to get:
x + y = 288 becomes:
5/7 * y + y = 288
multiply the second y by 7/7 to get 7/7 * y which is equivalent to y.
your equation becomes:
5/7 * y + 7/7 * y = 288
factor out the y to get:
(5/7 + 7/7) * y = 288
combine like terms to get:
12/7 * y = 288
multiply both sides of this equation by 7/12 to get:
y = 288 * 7 / 12
simplify to get:
y = 168
substitute for y in the first equation of x + y = 288 to get:
x = 120
your solution is:
x = 120 and y = 168
replace x and y in the original equations to confirm the answer is good.
x + y = 288 becomes 120 + 168 = 288 which becomes 288 = 288 which is true.
x/y = 5/7 becomes 120 / 168 = 5/7
simplify 120 / 168 by dividing numerator and denominator by 24 to get:
5/7 = 5/7 which is true.
x = 120 and y = 168 have been confirmed as good solutions so you're done.