if one-half of an integer is subtracted from three-fifths of the next consecutive integer, the difference is 3. What are the two integers?
i need help with this can anyone out there help me???? please
the inegers are the 2 that your trying to find the difference of...it makes no sense..you didn't finish writing the problem either..
(3/4)(x+1) - (1/2)x = 3
3(x+1) - 2x = 12
3x + 3 - 2x = 12
x = 9
So the two integers are 9 and 10
check:
3/4(10) - 1/2(9)
=15/2 - 9/2
= 3
5+(-8)=?
Of course! I can help you with that math problem. Let's break it down step by step.
First, let's define the variables:
Let's assume the first integer is 'x'.
The next consecutive integer would be 'x + 1' since we are dealing with consecutive integers.
According to the problem, we need to subtract half of the first integer from three-fifths of the next consecutive integer. So, we can write the equation as:
(3/5)*(x + 1) - (1/2)*x = 3
Next, let's simplify the equation:
(3/5)*(x + 1) - (1/2)*x = 3
(3/5)*x + (3/5)*(1) - (1/2)*x = 3
(3/5)*x + 3/5 - 1/2*x = 3
To compare fractions with different denominators, we need to find a common denominator. In this case, the common denominator would be 10. So, let's rewrite the equation:
(6/10)*x + 3/5 - 5/10*x = 3
Now, let's combine like terms:
(6/10)*x - (5/10)*x + 3/5 = 3
(1/10)*x + 3/5 = 3
To isolate 'x', let's subtract 3/5 from both sides of the equation:
(1/10)*x + 3/5 - 3/5 = 3 - 3/5
(1/10)*x = 3 - 3/5
Next, simplify the right side of the equation:
(1/10)*x = (15/5) - (3/5)
(1/10)*x = 12/5
To solve for 'x', multiply both sides of the equation by 10:
10*(1/10)*x = 10*(12/5)
x = 120/5
x = 24
Therefore, the first integer is 24. To find the next consecutive integer, add 1 to 24:
Next integer = x + 1 = 24 + 1 = 25
So, the two integers are 24 and 25.