The number of dimes inside the bag. Given: A bag contains quarters and dimes in...

Calculation:
Let the number of dimes in the bag be x.
Given that the quarters in the bag make $6. SInce 1 quarter is equivalent to $0.25, so the total number of quarters in the bag would be,
${\displaystyle \frac{6}{0.25}=24}$ quarters
Now given that the ratio of quarters and dimes in the bag is 3:5, so it gives
${\displaystyle \frac{\text{Number of quarters}}{\text{Number of dimes}}=\frac{3}{5}}$
${\displaystyle \frac{24}{x}=\frac{3}{5}}$
${\displaystyle 24\times 5=3\times x}$
${\displaystyle 120=3x}$
${\displaystyle x=\frac{120}{3}}$
${\displaystyle x=40}$
Thus, there are 40 dimes inside the bag.

Step 1
Given: ${\displaystyle \frac{6}{0.25}=24}$ quarters
The formula: ${\displaystyle \frac{\text{Number of quarters}}{\text{Number of dimes}}=\frac{3}{5}}$
${\displaystyle \frac{24}{x}=\frac{3}{5}}$
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5x, the least common multiple of x,5.
${\displaystyle 5\times 24=3x}$
Multiply 5 and 24 to get 120.
${\displaystyle 120=3x}$
Swap sides so that all variable terms are on the left hand side.
${\displaystyle 3x=120}$
Divide both sides by 3.
${\displaystyle x=\frac{120}{3}}$
Divide 120 by 3 to get 40.
${\displaystyle x=40}$

Step 1
For the equation
$\frac{24}{x}=\frac{3}{5}$
The cross product is
$25\times 5=x\times 3$
Solving for x
$x=\frac{24\times 5}{3}$
And reducing
x=40