Question

It's almost time to go home. You spent a lot of money this Vacation! you are counting up the money you have left. You only have dimes and quarters, and you have a total of 103 coins worth $15.25. How many dimes do you have? Solve Using Substatution

Answer 1

Start writing the equation of the number of coins

`q+d=103`

then, using the value of each coin write the equation for the amount of money you have

`0.25q+0.10d=15.25`

then, use the first equation to solve for d

`d=103-q`

substitute in the second equation

`\begin{gathered} 0.25q+0.10\cdot(103-q)=15.25 \\ \end{gathered}`

simplify and solve for q

`\begin{gathered} 0.25q+10.3-0.10q=15.25 \\ 0.15q=15.25-10.3 \\ 0.15q=4.95 \\ q=(4.95)/(0.15) \\ q=33 \end{gathered}`

find the value of d

`\begin{gathered} d=103-q \\ d=103-33 \\ d=70 \end{gathered}`