Question 832612
If Kim had 60 dimes and 62 more quarters than dimes, she would have
62 + 60 = 122 quarters
122 quarters = $30.50
60 dimes = $6.00
The total adds up to $36.50 , which is not the same as $50.50
 
{{{x}}}= number of dimes
If Kim had 62 more quarters than dimes,
{{{x+62}}}= number of quarters.
The value, in $, of {{{x}}} dimes plus {{{x+62}}} quarters is
{{{"0.10 x" + 0.25(x+62)}}} ,
so the equation to solve is
{{{0.10x+0.25(x+62)=50.50}}}
 
Solving:
{{{0.10x+0.25(x+62)=50.50}}}
{{{0.10x+0.25x+0.25*62=50.50}}}
{{{0.10x+0.25x+15.5=50.50}}}
{{{0.35x+15.5=50.50}}}
{{{0.35x=50.50-15.5}}}
{{{0.35x=35}}}
{{{x=35/0.35}}}
{{{highlight(x=100)}}}
 
Verifying:
If Kim had 100 dimes and 62 more quarters than dimes, she would have
62 + 100 = 162 quarters
162 quarters = $40.50
100 dimes = $10.00
The total is $40.50 + $10.00 , which is $50.50.