Question 538031
Currently Karen is 4 times as old as Lucy. Six years from now, Karen will be 3 times as old as Lucy.
 How old is Lucy now? 
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Let's do it this way
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Let L = Lucy's age now
Let K = Karen's age now
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Write an equation for each statement:
"Karen is 4 times as old as Lucy."
K = 4L
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"Six years from now, Karen will be 3 times as old as Lucy"
K + 6 = 3(L + 6)
K + 6 = 3L + 18
K = 3L + 18 - 6
K = 3L + 12
Replace K with 4L (from the 1st statement)
4L = 3L + 12
4L - 3L = 12
L = 12 yrs is Lucy's age now
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Check our solution in the given statement: (Karen = 4(12) = 48)
"Six years from now, Karen will be 3 times as old as Lucy"
48 + 6 = 3(12+6)
54 = 3(18)