Question 105775
The problem says dimes AND quarters, so I can assume that it is not ALL dimes
or ALL quarters.
Let D equal the number of dimes
Let Q equal the number of quarters
{{{.1D = 30}}} This is if ALL the coins were dimes
{{{D = 300}}}
{{{.25Q = 30}}} This is if ALL the coins were quarters
{{{Q = 120}}}
But I know these are not true. What I do know is:
{{{D < 300}}}
and
{{{Q < 120}}}
So,
{{{.1D < 30}}} and
{{{.25Q < 30}}}
I can add these inequalities
{{{.1D + .25Q < 60}}}
Note that if D=300 and Q=120, then I get 60<60, but
numbers less than these for D or Q is less than 60