Question

Bob has 16 coins totaling $1.20. If he only has dimes (10 cents) and nickels (5 cents), how many of each coin does he have?Bob has_ nickels and _ dimes.

Answer 1

Bob has 8 nickels and 8 dimes.

Explanation:

• Let the number of dimes bob has = d

,

• Let the number of nickels bob has = n

Bob has a total of 16 coins, therefore:

`\begin{gathered} d+n=16 \\ \implies d=16-n\cdots(1) \end{gathered}`

Next, it is given that the total worth of the coins is $1.20.

`0.1d+0.05n=1.20\cdots(2)`

Solve equation (1) and (2) simultaneously:

`\begin{gathered} 0.1d+0.05n=1.20 \\ 0.1(16-n)+0.05n=1.20 \\ 1.6-0.1n+0.05n=1.20 \\ 1.6-1.20=0.1n-0.05n \\ 0.4=0.05n \\ n=(0.4)/(0.05) \\ n=8 \end{gathered}`

Finally solve for d:

`d=16-n=16-8=8`

Bob has 8 nickels and 8 dimes.