Question 215265
Write 2 Equations based on the information given. Let V=Vivian's age and C=Carmen's age:
From the first sentence:
Equation #1:{{{V=C+5}}}
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From the second sentence:
{{{4C-2V=C+10}}}
Simplify:
Equation #2:{{{3C-2V=10}}}
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Now you have 2 equations with 2 unknowns. 
Substitute Equation #1 into Equation #2:
{{{3C-2(C+5)=10}}}
Solve for C:
{{{3C-2C-10=10}}}
{{{highlight(C=20)}}}
Next, plug this value of C into Equation #1 and solve for V:
{{{highlight(V=25)}}}
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As a final check, plug these results back into Equation #1 and Equation #2 to be sure they still hold true. I'll leave that part to you.
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Good Luck,
tutor_paul@yahoo.com