SOLUTION: 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

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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