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.
Just did that, see above
Old price:36 cents
new price:45 cents
To solve this problem, let's assign variables to the unknown prices.
Let:
- x be the old price of salt
- y be the new price of salt
According to the given information, "The price of salt goes up by 9 cents," we can set up the equation:
y = x + 9
Next, the problem states, "The old price goes up by four-fifths of the new price." This means that the old price (x) is increased by four-fifths (or 4/5) of the new price (y). Mathematically, this can be represented as:
x + 4/5 * y = ?
To find the actual equation, we need to substitute the value of y from the first equation into the second equation:
x + 4/5 * (x + 9) = ?
Now, we can solve for x.
Multiply 4/5 by each term inside the parentheses:
x + 4/5 * x + 4/5 * 9 = ?
Simplify the equation:
x + (4/5) * x + (36/5) = ?
Combine like terms:
(9/5) * x + (36/5) = ?
To remove the fraction, we can multiply the entire equation by 5:
5 * [(9/5) * x + (36/5)] = 5 * ?
Simplify:
9x + 36 = ?
Now, we can solve for x by isolating x:
9x = ? - 36
9x = ? - 36
Finally, divide both sides of the equation by 9:
x = (? - 36) / 9
After finding the value of x, we can substitute it back into the first equation to find y.