Question 980978: PLEASE HELP.
John and Marie went to collect mangoes. At the end of the trip John said “Marie give me 7 of yours and I will have two times what you have”. Marie replied, “No John, you give me seven of yours and we will have the same amount”. Find the number of mangoes that each one collected.
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website!
Let x be the number of mangoes that John collected,
and let y be the number of mangoes that Marie collected.
If Marie gives 7 mangoes to John, then Jon will have (x+7) mangoes and Marie will have (y-7) mangoes. According to the condition,
x + 7 = 2(y-7).
In opposite, if John gives 7 mangoes to Marie, then Marie will have (y+7) mangoes and John will have (x-7) mangoes. Again, according to the second condition,
y + 7 = x - 7.
Thus you get the system of two linear equations in two unknowns
 .
To solve it, express y from the second equation
y = x - 14
and substitute it to the first equation
x + 7 = 2((x-14) - 7),
x + 7 = 2x - 28 - 14,
x = 7 + 14 + 28 = 49.
Thus John collected 49 mangoes.
Marie collected y = x - 14 = 49 - 14 = 35 mangoes.
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