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: P says to Q, “if you give me 10 of your apples, I will have twice the number of apples left with you”.
Then, we have
p + 10 = 2(q - 10)
p + 10 = 2q - 20
Subtract 2q and 10 from each side.
p - 2q = - 30 -----(1)
Given : Q says to P, “if you give me 10 of your apples, I will the same number of apples as left with you.”
Then, we have
q + 10 = p - 10
Subtract p and 10 from each side.
- p + q = - 20 -----(2)
In order to eliminate p in (1) and (2), add (1) and (2).
- q = - 50
Multiply each side by (-1).
q = 50
Substitute 50 for q in (1).
(1)-----> p - 2(50) = - 30
p - 100 = - 30
Add 100 to each side.
p = 70
So, P and Q originally have 70 and 50 apples respectively.
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