Question 1041634
I can imagine the struggle. The sticking point here is
that GPA is being applied to certain restricted grades
( GPA = grades / credits )
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Nelson transferred 20 credits with a GPA of 1.5.
{{{ 1.5 = g[1] / 20 }}}
{{{ g[1] = 30 }}}
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Then you are told:
{{{ 1.9 = g[2] / 25 }}}
{{{ g[2] = 47.5 }}}
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Overall GPA = {{{ ( g[1] + g[2] ) / ( 20 + 25 ) }}}
Overall GPA = {{{ ( 30 + 47.5 ) / 45 }}}
Overall GPA = {{{ 77.5/45 }}}
Overall GPA = {{{ 1.722 }}}
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How many credits with a 2.5 average would he 
need to raise his GPA to a 2.0?
Let {{{ n }}} = number of credits with 2.5 GPA needed
{{{ 2.5 = g[3] / n }}}
{{{ g[3] = 2.5n }}}
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New Overall GPA = {{{ ( g[1] + g[2] + g[3] ) / ( 20 + 25 + n ) }}}
{{{ 2.0 = ( 30 + 47.5 + 2.5n ) / ( 45 + n ) }}}
{{{ 2.0 = ( 77.5 + 2.5n ) / ( 45 + n ) }}}
{{{ 90 + 2n = 77.5 + 2.5n }}}
{{{ .5n = 12.5 }}}
{{{ n = 25 }}}
He needs 25 credits with GPA = 2.5 to raise his GPA to 2.0
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You could call the GPAs GPA[1], GPA[2], GPA[3] and
the number of credits they apply to n[1], n[2], n[3]
and grades that you get from that
n[1] * GPA[1],  n[2]*GPA[2],  n[3]*GPA[3]
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Hope I got it and didn't further confuse