Answer:To find the discounted price of the washer, we can set up a proportion based on the price ratios given in the problem.
The initial price ratio of the washer to dryer is 5:2. This means that for every $5 the washer costs, the dryer costs $2.
After a discount of $50 on each item, the new price ratio of the washer to dryer is 55:19. This means that for every $55 the washer costs, the dryer costs $19.
To set up the proportion, we can use the fact that the discount is the same for both items. Let's assume the initial price of the washer is W and the initial price of the dryer is D.
Since the price ratio of the washer to dryer is 5:2, we have the equation:
W/D = 5/2
After the discount, the price ratio becomes 55:19, so we have the equation:
(W - 50)/(D - 50) = 55/19
Now we can solve for the discounted price of the washer.
First, cross-multiply the equations to eliminate the denominators:
2W = 5D
19(W - 50) = 55(D - 50)
Expand the second equation:
19W - 950 = 55D - 2750
Now, let's solve for W in terms of D:
2W = 5D
W = (5D)/2
Substitute this value into the second equation:
19[(5D)/2] - 950 = 55D - 2750
Simplify the equation:
(95D)/2 - 950 = 55D - 2750
Multiply through by 2 to eliminate the fraction:
95D - 1900 = 110D - 5500
Combine like terms:
-15D = -3600
Divide by -15 to solve for D:
D = 240
Now substitute this value back into the equation for W:
W = (5D)/2
W = (5*240)/2
W = 1200/2
W = 600
So, the initial price of the washer is $600.
After a discount of $50, the discounted price of the washer is $600 - $50 = $550.
Therefore, the discounted price of the washer is $550.