Operation: Fixing The Operation

Algebra Level 1

X + Y = 42 X + Y = 42

X − Y = 24 X - Y = 24

A + B = 69 A + B = 69

A − B = 15 A - B = 15

X Y + A B = ? XY + AB = \, ?

Note: Each variable/letter corresponds to one distinct positive integer.

Express your answer as the sum of XY and AB

1431 42 120 1337

Christian Zedrick Jumawan by Christian Zedrick Jumawan , 35

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1 solution

Ralph James
Apr 2, 2016

X + Y + ( X − Y ) = 42 + 24 ⟹ 2 X = 66 ⟹ X = 33 , Y = 9 , X Y = 297 X + Y + (X - Y) = 42 + 24 \implies 2X = 66 \implies X = 33, Y = 9, XY = 297 A + B + ( A − B ) = 69 + 15 ⟹ 2 A = 84 ⟹ A = 42 , Y = 27 , A B = 1134 A + B + (A - B) = 69 + 15 \implies 2A = 84 \implies A = 42, Y = 27, AB = 1134 X Y + A B = 1134 + 297 = 1431 XY + AB = 1134 + 297 = \boxed{1431}

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Exactly. :D

Christian Zedrick Jumawan - 5 years, 2 months ago

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