Question 913748
{{{t}}}= years since 1953.
{{{W(t)}}}= Frank's weight at time {{{t}}} (in pounds).
{{{W[0]}}}= Frank's weight (in pounds) at {{{t=0}}} (1953).
{{{W(t)=W[0]+2t}}} , because he's been gaining 2 pounds per year since 1953.
 
For 1983:
{{{t=1983-1953=30}}} and Frank's weight that year is
{{{W(30)=W[0]+2*30=W[0]+60}}} .
The problem tells us that {{{W(30)=W[0]+60}}} is 140% of Frank's 1953 weight, or {{{1.40W[0]}}} , so
{{{1.40W[0]=W[0]+60}}} is our first equation.
{{{1.40W[0]=W[0]+60}}}--->{{{1.40W[0]-W[0]=60}}}--->{{{(1.4-1)W[0]=60}}}--->{{{0.4W[0]=60}}}--->{{{W[0]=60/0.4}}}--->{{{W[0]=150}}} .
So Frank weighed {{{W[0]=150}}}{{{pounds}}} in 1953,
and he gained 2 pound per year after that, so
{{{W(t)=150+2t}}}
 
For 1998:
{{{t=1998-1953=45}}} and Frank's weight that year is
{{{W(45)=150+2*45}}}--->{{{W(45)=150+90}}}--->{{{W(45)=240}}} .
So Frank weighed {{{W[45]=240}}}{{{pounds}}} in 1998.
 
For 1988:
{{{t=1988-1953=35}}} and Frank's weight that year is
{{{W(35)=150+2*35}}}--->{{{W(45)=150+70}}}--->{{{W(45)=220}}} .
So Frank weighed {{{W[35]=220}}}{{{pounds}}} in 1988.
 
What fraction and what percentage of {{{240}}} is {{{220}}} ?
As a fraction, it is {{{220/240=11/12= "0.91666 ..."}}} .
As a percentage, it is {{{"91.666 ..."}}}{{{"%"}}} = about {{{highlight("92 %")}}}