Question

2/5 of the cost of a guitar is equal to 1/4of the cost of a violin .if the violin costs $405 more than the guitar find the total cost of musical instruments

Answer 1

Let the cost of guitar be x and the cost of violin be y
Now according to the first analogy,
$\frac{2x}{5} = \frac{y}{4}$
Which gives
$8x = 5y \\ 8x - 5y = 0$
Second analogy gives
$x + 405 = y$
Substitute this in the first equation
$8x - 5(x + 405) = 0 \\ 8x - 5x - 2020 = 0 \\ 3x = 2020 \\ x = 673.33$
Now
$y = 673.33 + 405 = 1078.33$