the difference of two numbers is 5. three times the smaller number is two more than twice the larger number. find the numbers
a = b + 5
3a = 2b + 2
Substitute b + 5 for a in the second equation and solve for b. Put that value in the first equation to find a. Put both values in the second equation as a check.
that didn't work
I'm sorry, b is the smaller number. The second equation should be:
3b = 2a + 2
Try it again.
The different of X-y=5, let x be the small and y be the large , three time the smaller=3x = two more than twice the large=2y+2, we are going to find con the first equation x=y+5 now we are going to plug that value of x in our second equation, 3x=2y+2, 3(y+5)=2y+2, 3y+15=2y+2, y=-15+2, y=-13, now let find x, x-13=5x=+13+5=18,!our number are -13 and18
To solve this problem, let's first assign variables to the unknown numbers. Let's call the larger number "x" and the smaller number "y".
According to the problem, the difference of two numbers is 5, so we can set up the following equation:
x - y = 5 ...(Equation 1)
The problem also states that three times the smaller number is two more than twice the larger number. This can be represented by the equation:
3y = 2x + 2 ...(Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) with two variables (x and y). We can solve this system of equations to find the values of x and y.
Let's start by rearranging Equation 1 to solve for x:
x = y + 5 ...(Equation 3)
Substitute Equation 3 into Equation 2:
3y = 2(y + 5) + 2
Now, solve for y:
3y = 2y + 10 + 2
3y - 2y = 12
y = 12
Now, substitute the value of y back into Equation 3 to find x:
x = 12 + 5
x = 17
Therefore, the larger number (x) is 17 and the smaller number (y) is 12.
So, the answer is:
The larger number is 17, and the smaller number is 12.