Nickels and dimes

Bob has a handful of nickels and dimes worth $2.45. How many dimes are there if there are 4 more nickels than dimes?

Hint: A nickel is worth 5 cents, and a dime is worth 10 cents. So, one dime is worth the same as two nickels.

Correct answer:

a =  15

Step-by-step explanation:

$$\begin{gathered} 0.10a+0.05b=2.45 \\ b=a+4 \\ 0.10\cdot a+0.05\cdot b=2.45 \\ b=a+4 \\ 0.1a+0.05b=2.45 \\ a-b=-4 \\ Pivot:Row1\leftrightarrow Row2 \\ a-b=-4 \\ 0.1a+0.05b=2.45 \\ Row2-0.1\cdot Row1\to Row2 \\ a-b=-4 \\ 0.15b=2.85 \\ b=\frac{2.85}{0.15}=19 \\ a=-4+b=-4+19=15 \\ a=15 \\ b=19 \end{gathered}$$

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