I have just one math problem that I need a little help with. Please give me the answer, and walk me through it, too, to help me understand it. Thanks!
The price of a ring is decreased by 40% and the resulting price is increased by 50%. The final price is $360. What was the original price?
I've tried this problem a few times, but I haven't gotten any good answers yet.
Again, thanks so much! I appreciate your help!
let the original price be $x
so after the first reduction of 40%, the new price is .6x
now this is cut in half (50%)
so the new price is .3x
.3x = 360
x = 360/.3
= 1200
so the original price was $1200
check: 40% of 1200 = 480 leaving 720
now 50% of 720 = 360
To find the original price, we can break down the problem into steps and use algebraic expressions:
Step 1: Let's assume the original price of the ring is represented by the variable "x".
Step 2: The price of the ring is decreased by 40%. This means we need to find 40% of the original price and subtract it: 0.40x.
The new price after the decrease is then: x - 0.40x = 0.60x.
Step 3: The resulting price from step 2 is then increased by 50%. We need to find 50% of the new price and add it: 0.50 * 0.60x = 0.30x.
The final price is now: 0.60x + 0.30x = 0.90x.
Step 4: We know that the final price is $360, so we can set up the equation: 0.90x = 360.
Step 5: To find the original price, we need to isolate the variable x. Divide both sides of the equation by 0.90:
0.90x / 0.90 = 360 / 0.90.
Simplifying, we get:
x = 400.
Therefore, the original price of the ring was $400.
By following these steps and using algebraic expressions, we can find the original price of the ring.