Question

John has a total of $\$4.30$ in dimes (1 dime $=\$0.10$) and quarter (1 quarter $=\$0.25$), and he has 19 coins in total. Which of the following systems of equations can be used to find the number of dimes, $d$ and the number of quarters, $q$ he has?

• A. $d+q=19$
  $0.1d+0.25q=4.30$
• B. $d+q=4.30$
  $0.1d+0.25q=19$
• C. $0.1d+0.25q=19$
  $10d+25q=4.30$
• D. $0.1d+0.25q=19$
  $25d+10q=4.30$

Answer 1

The correct option is A $d+q=19$

$0.1d+0.25q=4.30$
We know that 1 dime is same as $\$0.10$ and that 1 quarter is the same as $\$0.25$. Therefore, we can write the following equation to show that all the dimes and quarters makes $\$4.30$
$0.1d+0.25q=4.30$
If there are 19 coins in total, then we can create the following equation:
$d+q=19$
We can use the following system of equations to describe this situation:
$d+q=19$
$0.1d+0.25q=4.30$
The correct answer is option A.