If 9 is subtracted from half a certain number the result is the same as when 1/3 is added to the numbers. Find the number
Let's call the certain number "x".
According to the problem, "9 is subtracted from half a certain number" can be written as:
1/2x - 9
And "1/3 is added to the number" can be written as:
x + 1/3
The problem tells us these two expressions are equal, so we can set them equal to each other and solve for x:
1/2x - 9 = x + 1/3
To solve for x, we'll start by getting rid of the fractions. We can do this by multiplying both sides of the equation by the least common multiple of the two denominators, which is 6:
6(1/2x - 9) = 6(x + 1/3)
3x - 54 = 6x + 2
Next, we'll isolate the variable on one side of the equation. Let's subtract 3x from both sides:
-54 = 3x + 2
Subtracting 2 from both sides:
-56 = 3x
Finally, dividing both sides by 3:
x = -56/3 or approximately -18.67
So the certain number we're looking for is -18.67.
Find the nearest kobo the compounding interest on #3000 for years at 3% per annum.
To find the compounding interest on #3000 for 2 years at 3% per annum, we can use the formula:
A = P(1 + r/n)^(nt)
where:
- A is the total amount after t years
- P is the principal amount (which is #3000 in this case)
- r is the annual interest rate (which is 3% or 0.03 as a decimal)
- n is the number of times the interest is compounded per year (since the problem doesn't specify, we'll assume it's compounded annually which means n = 1)
- t is the number of years (which is 2 in this case)
Plugging in the values, we get:
A = 3000(1 + 0.03/1)^(1*2)
A = 3000(1.03)^2
A ≈ #3258.09
So the total amount after 2 years, including the interest, is approximately #3258.09.
To find the compounding interest, we can subtract the principal from the total amount:
I = A - P
I ≈ #258.09
Therefore, the compounding interest on #3000 for 2 years at 3% per annum is approximately #258.09.
To find the nearest kobo, we can round this to the nearest hundredth of a naira, which is #0.01. Therefore, the nearest kobo would be #25.81 (or rounding down to #25.80).
Solve the system of the equation 5x * 5-y=25 and 4x *8-y=32
There seems to be some missing information or incorrect syntax in the equations. It's not clear what the variables are and where the multiplication symbols are supposed to be. Here are a couple of possible interpretations of the equations and their solutions:
Interpretation 1:
Assuming the variables are x and y and the multiplication symbols should be asterisks:
5x * 5 - y = 25 (equation 1)
4x * 8 - y = 32 (equation 2)
We can start by simplifying the left-hand sides of both equations:
25x - y = 25 (simplifying equation 1)
32x - y = 32 (simplifying equation 2)
Now we have a system of two linear equations with two variables. To solve for x and y, we can use the method of substitution or elimination. Since the coefficients of y are the same in both equations, we can eliminate y by subtracting the second equation from the first:
25x - 32x - y + y = 25 - 32
-7x = -7
x = 1
Now we can substitute x = 1 into either equation to find y:
25(1) - y = 25 (from equation 1)
-y = 0
y = 0
Therefore, the solution to the system of equations is x = 1 and y = 0.
Interpretation 2:
Assuming the variables are x and y and there shouldn't be any multiplication symbols:
5x + 5 - y = 25 (equation 1)
4x + 8 - y = 32 (equation 2)
We can simplify the left-hand sides of both equations:
5x - y = 20 (simplifying equation 1)
4x - y = 24 (simplifying equation 2)
Now we can use the method of substitution or elimination to solve for x and y. For example, we can eliminate y by subtracting the second equation from the first:
5x - 4x - y + y = 20 - 24
x = -1
Now we can substitute x = -1 into either equation to find y:
5(-1) - y = 20 (from equation 1)
-y = 25
y = -25
Therefore, the solution to the system of equations is x = -1 and y = -25.
Let's call the certain number x.
According to the given information:
Half the certain number minus 9 is equal to one-third added to the number.
So we can write the equation:
(x/2) - 9 = x + (1/3)
To solve the equation, first, let's get rid of the fractions by multiplying every term by 6 (the least common denominator of 2 and 3):
6[(x/2) - 9] = 6[x + (1/3)]
Simplifying the equation:
3x - 54 = 6x + 2
Next, let's isolate the variables:
Subtracting 3x from both sides:
-54 = 3x + 2
Subtracting 2 from both sides:
-56 = 3x
Dividing both sides by 3:
-56/3 = x
Therefore, the certain number is -56/3 or -18.67 (rounded to two decimal places).
To solve this problem, we need to translate the given information into an equation. Let's suppose the certain number is represented by the variable "x".
According to the problem, when 9 is subtracted from half of the number, we get the same result as when 1/3 is added to the number. Mathematically, this can be expressed as:
(1/2)x - 9 = x + (1/3)
Now let's solve for x:
To get rid of the fractions, we can multiply the entire equation by the least common denominator (LCD) of 2 and 3, which is 6:
6 * ((1/2)x - 9) = 6 * (x + (1/3))
Simplifying this equation gives us:
3x - 54 = 6x + 2
Next, we move all terms involving x to one side of the equation by subtracting 3x from both sides:
-54 = 6x - 3x + 2
Simplifying further:
-54 = 3x + 2
Next, we move the constant term to the other side of the equation by subtracting 2 from both sides:
-54 - 2 = 3x + 2 - 2
Simplifying further:
-56 = 3x
Lastly, we solve for x by dividing both sides by 3:
(-56) / 3 = 3x / 3
Simplifying gives us:
x = -56/3
So, the certain number is -56/3 or approximately -18.67.