Question

Remember to write a let statement and answer the question. A collection of dimes abs quarters has a value of $1.35. List all possible combinations of dimes abs quarters.

Answer 1

Let d represents dimes and q represents quarter.

Note that a dime is 10 cent, which is same as one over ten, and a quarter is one over four

`\begin{gathered} d=(1)/(10)=0.1 \\ q=(1)/(4)=0.25 \end{gathered}`

Given that a collection of dimes abs quarters has a value of $1.35, then this can be represented as below:

`0.1d+0.25q=1.35`

Multiply through by 100 to get

`\begin{gathered} 100*0.1d+100*0.25q=100*1.35 \\ 10d+25q=135 \end{gathered}`

To get the possible combinations of dimes and quarters, lets the try different values of that will satisfy the equation.

When q is 1,

`\begin{gathered} 10d+25q=135 \\ q=1 \\ 10d+25(1)=135 \\ 10d+25=135 \\ 10d=135-25 \\ 10d=110 \\ d=(110)/(10)=11 \end{gathered}`

Therefore, 11 dimes and 1 quarter abs is a possible combination

When q is 3

`\begin{gathered} 10d+25(3)=135 \\ 10d+75=135 \\ 10d=135-75 \\ 10d=60 \\ d=(60)/(10) \\ d=6 \end{gathered}`

Also, 6 dimes and 3 quarter abs is a possible combination

When q is 5

`\begin{gathered} 10d+25(5)=135 \\ 10d+125=135 \\ 10d=135-125 \\ 10d=10 \\ d=(10)/(10) \\ d=1 \end{gathered}`

Also, 1 dime and 5 quarter abs is a possible combination

When q is 7

`\begin{gathered} 10d+25(7)=135 \\ 10d+175=135 \\ 10d=135-175 \\ 10d=-40 \\ d=(-40)/(10)=-4 \end{gathered}`

Since negative answer was gotten for dimes, 7 quater wouldn't give any possible combination.

Hence, there are It can be found that there are there are three possible combinations, these are:

11 dimes and 1 quarter abs

6 dimes and 3 quarter abs

1 dime and 5 quarter abs