Question 410283
Let {{{t}}} = Terri's age
Let {{{g}}} = Ginnie's age
Let {{{j}}} = Joan's age
given:
{{{t = g + 2}}}
{{{j = 2g}}}
{{{t^2 + g^2 + j^2 = 420}}}
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{{{(g + 2)^2 + g^2 + (2g)^2 = 420}}}
{{{g^2 + 4g + 4 + g^2 + 4g^2 = 420}}}
{{{6g^2 + 4g - 416 = 0}}}
{{{3g^2 + 2g - 208 = 0}}}
Use quadratic formula
{{{g = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 3}}}
{{{b = 2}}}
{{{c = -208}}}
{{{g = (-2 +- sqrt( 2^2-4*3*(-208) ))/(2*3) }}}
{{{g = (-2 +- sqrt( 4 + 2496 ))/ 6 }}}
{{{g = (-2 + 50)/ 6 }}}
{{{g = 48/6}}}
{{{g = 8}}}
and
{{{j = 2g}}}
{{{j = 16}}}
and
{{{t = g + 2}}}
{{{t = 10}}}
Ginnie is 8 yrs old
check answer:
{{{t^2 + g^2 + j^2 = 420}}}
{{{10^2 + 8^2 + 16^2 = 420}}}
{{{100 + 64 + 256 = 420}}}
{{{420 = 420}}}
OK