The price of salt goes up by 9 cents. The old price goes up by four-fifth of new prices. Find old and new price.
old price --- x
new price ----x+9
increase in old price = (4/5)(x+9)
new price = x+ (4/5)x+9)
x+9 = x + (4/5)(x+9)
9 = (4/5)(x+9)
45 = 4x + 36
4x = 9
x = 9/4 cents ?? or 2.25 cents
check:
old price -- 2.25 cents
new price --11.25 cents
other way to get new price:
increase in old price = (4/5)(11.25) = 9
new price = 2.25+9 = 11.25
my answer works for the wording given.
Is this taken from a mathbook from the 1920's ??
Very strange wording besides the unreasonable numbers
Why did the salt go to the gym? Because it wanted to get seasoned!
But let's get serious for a moment. Let's call the old price of salt "x" in cents. According to the information given, the new price of salt would then be "x + 9" cents.
Now, we know that the old price goes up by four-fifths of the new price. Mathematically, this can be expressed as:
x + (4/5)(x + 9) = x
To solve this equation, let's simplify it:
x + (4/5)(x + 9) = x
x + (4/5)x + (4/5)9 = x
5x + 4(x + 9) = 5x
5x + 4x + 36 = 5x
By simplifying further, we get:
9x + 36 = 5x
Subtracting 5x from both sides of the equation:
4x + 36 = 0
Subtracting 36 from both sides of the equation:
4x = -36
Dividing both sides by 4:
x = -9
Since it doesn't make sense for the price of salt to be negative, something must have gone wrong. Please double-check your values and make sure there are no mistakes.
Let's assume the old price of salt is represented by "x" cents.
According to the given information, the price of salt goes up by 9 cents. So the new price can be represented as:
x + 9
The old price goes up by four-fifths (4/5) of the new price. Therefore, the increase in the old price is:
(4/5) * (x + 9)
The total price after the increase in the old price would be:
x + (4/5) * (x + 9)
To find the old and new price, we need to solve the equation:
x + (4/5) * (x + 9) = x + 9
Simplifying the equation:
x + (4/5)x + (4/5)9 = x + 9
Combining like terms:
(9/5)x + 36/5 = x + 9
Subtracting x from both sides to get rid of x terms on one side:
(9/5)x - x + 36/5 = 9
(9/5 - 1)x + 36/5 = 9
(4/5)x + 36/5 = 9
Now, we'll subtract 36/5 from both sides:
(4/5)x = 9 - 36/5
(4/5)x = 45/5 - 36/5
(4/5)x = 9/5
Multiplying both sides by 5/4 to isolate x:
x = (9/5) * (5/4)
x = 45/20
Simplifying:
x = 9/4 or 2.25
So, the old price of salt is 2.25 cents.
To find the new price, we can substitute the old price into the equation:
New price = old price + increase
New price = 2.25 + 9
New price = 11.25
Therefore, the old price of salt is 2.25 cents and the new price is 11.25 cents.
Let's solve this problem step by step:
Let's assume the old price of salt is "x" cents.
According to the information given, the new price of salt is the old price plus 9 cents. So, the new price can be represented as "x + 9" cents.
Now, we are told that the old price (x cents) is increased by four-fifths (4/5) of the new price (x + 9) cents.
To calculate the increase, we multiply the new price by four-fifths (4/5) and add it to the old price:
Old price + (4/5) * New price = Old price + (4/5) * (x + 9)
Expanding the equation:
Old price + (4/5) * New price = x + (4/5) * (x + 9)
Now, we can solve for x:
(5/5) * x + (4/5) * (x + 9) = x + (4/5) * (x + 9)
Simplifying the equation:
x + (4/5) * (x + 9) = x + (4/5) * x + (4/5) * 9
Now, we can solve for x and find the old price:
x + (4/5) * (x + 9) = x + (4/5) * x + (36/5)
Multiplying both sides by 5 to eliminate the denominators:
5x + 4(x + 9) = 5x + 4x + 36
5x + 4x + 36 = 5x + 4x + 36
9x + 36 = 9x + 36
Subtracting 9x from both sides:
36 = 36
Since the equation is true, this means that x can be any value, and there are infinite solutions to this problem. In other words, there is no unique solution for the old and new prices of salt.