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

$\begin{gathered} d=\frac{1}{10}=0.1 \\ q=\frac{1}{4}=0.25 \end{gathered}$

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

$\begin{gathered} 100\times0.1d+100\times0.25q=100\times1.35 \\ 10d+25q=135 \end{gathered}$

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

When q is 1,

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

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

When q is 3

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

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

When q is 5

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

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

When q is 7

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

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