Question 110637
When setting up equations to solve word problems, it is often a good idea to define the variable(s) to represent the quantity or quantities we want to discover.  In this problem, you only need to calculate one quantity, namely some number of years in the past.  Let that be x.
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So x years ago, Grandpa was 66 - x years old, and Carlos was 12 - x years old, and we know that {{{66-x=10(12-x)}}}
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Now all we need to do is solve for x:
{{{66-x=10(12-x)}}}
{{{66-x=120-10x}}}
{{{-x+10x=120-66}}}
{{{9x=54}}}
{{{x=6}}}
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So, 6 years ago, Grandpa was 10 times older than Carlos.
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Check:
:
66-6 = 60, and 12 - 6 = 6, and 6 * 10 = 60.  Check!