Each year a computer part is worth about 3/4 of its value the previous year. Now a certain part is worth $90. What was its value two years ago? :-/



Would this be 135 dollars?

Hmmm... I get $160... if y=current value and x=previous year's value, then y=(3/4)x. You start with $90...

90=(3/4)x
x=(4/3)(90)
x=120

... so it was 120 one year ago, and...

120=(3/4)x
x=(4/3)(120)
x=160

... so it was $160 two years ago.

Okay just make an equation:
first you need some variables, the first variable will be X and that's how much money you have, then Y and that's how much money you will have, and lastly n and that's how many years.
1. for every year you multiply the money you have by 3/4
so 3/4 to the power of years gives you the factor to multiply the money you have by.
2. X how much money you have when you start must be multiplied by (3/4)^n so that your final amount of money can be obtained.
3. Y equals your final amount of money

So this is how the equation would look like:
Y=(3/4)^n *X
After 2 years you end up with $90.00 so the final amount of money (Y) equals $90.00, and the amount of years (n) equals 2. 90=(3/4)^2 *X Solve for X
90=(9/16)*X
X*9=.1440
X=160
The original value was $160.00

Let x be the value two years ago

Then in one year it is worth (3/4)x
In two years it is worth (3/4)[(3/4)x]

This equals (3/4)^2 * x and we know that it also
equals $90

So solve for x in (3/4)^2 * x = $90

(9/16) x = $90

x/16 = $10

x = $160

Quote:

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Each year a computer part is worth about 3/4 of its value the previous year. Now a certain part is worth $90. What was its value two years ago?    :-/



Would this be 135 dollars?

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yes this would

The item was worth $160 two years ago based on what is called the "diminishing value method".

I can see how you thought it might be $135. You added a quarter of $90 twice to get to $135.

If an item loses a quarter of its value from the previous year, you can use this formula:

Multiply the item's current value by 4/3 then multiply the result by 4/3 again to arrive at the value two years ago.

Current value of $90 times 4/3 = $120
$120 times 4/3 = $160

The Fernandez family is making shelves to hang on wall brackets for the three kids' bedrooms. They bought a 4 feet by 8 feet sheet of plywood to cut into shelves 24 inches long by 8 inches deep. This would make the correct number of shelves, with no wood left over. They also bought some trime to edge the shelves.

They are making Ricardo 3/4 as many shelves as they are making for Anthony. Maria is getting four more shelves than her brother Ricardo.

How many shelves are being made for each person?

I know that the total shelves being made is 24 but I'm not sure about how many each person is getting. :confused:

Quote:

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Originally Posted by angel031792

The Fernandez family is making shelves to hang on wall brackets for the three kids' bedrooms. They bought a 4 feet by 8 feet sheet of plywood to cut into shelves 24 inches long by 8 inches deep. This would make the correct number of shelves, with no wood left over. They also bought some trime to edge the shelves.

They are making Ricardo 3/4 as many shelves as they are making for Anthony. Maria is getting four more shelves than her brother Ricardo.

How many shelves are being made for each person?

i know that the total shelves being made is 24 but im not sure about how many each person is getting. :confused:

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Make an equation like this:
Amount of shelves Anthony gets = X
Ricardo = (3/4)*X
Maria = (3/4)*X + 4

Now, Anthony + Ricardo + Maria = 24 which means that
X + (3/4)*X + (3/4)*X + 4 = 24
(5/2)*X = 20
X = 20 * (2/5) = 8

So, Anthony gets 8 shelves.
Ricardo gets (3/4)*8 = 6
Maria gets "Ricardo" + 4 = 10

To check the result, we add 10 + 6 + 8 = 10 + 14 = 24

So our calculation is correct.