To solve this problem we need to use the conditions to write an equation, so Q will be the number of quarters and D will be the number of dimes so the first condition is:
the sum of quartes (0.25) plus dimes (0.10) are $1.15
[tex]Q(0.25)+D(0.10)=1.15[/tex]the second condition is; she has one more dimes than quarters so:
[tex]Q+1=D[/tex]So we can replace the secon equation into the first equation so:
[tex]Q(0.25)+(Q+1)(0.10)=1.15[/tex]Now we can simplify the equation so:
[tex]0.25Q+0.10Q+0.10=1.15[/tex]And finally we solve for Q so:
[tex]\begin{gathered} 0.35Q=1.15-0.10 \\ 0.35Q=1.05 \\ Q=\frac{1.05}{0.35} \\ Q=3 \end{gathered}[/tex]Now we can replace the value of Q in the second equation so:
[tex]\begin{gathered} D=Q+1 \\ D=3+1 \\ D=4 \end{gathered}[/tex]So Francesca have 3 quarters and 4 dimes
