sorry but i have 1 more question...
the sum of two numbers is 30. If three times the greater number is subtracted by 2 times the lesser number, the result is 30. What is the product of the two numbers?...
SORRY! ^^"
thank you.
N+M=30
3N-2M=30
solve for N and M.
Then the product is N*M
No problem! Let's solve the problem step-by-step.
Let's assume one of the numbers is x and the other number is y.
According to the problem, the sum of the two numbers is 30, so we can form the equation:
x + y = 30 --- Equation 1
The problem also states that three times the greater number (which we can assume is x) is subtracted by 2 times the lesser number (which we can assume is y), resulting in 30. We can form the equation:
3x - 2y = 30 --- Equation 2
To find the product of the two numbers (xy), we need to find the values of x and y that satisfy both equations.
We can solve this system of equations using a method called substitution or elimination.
Let's use the substitution method. We can solve Equation 1 for x:
x = 30 - y
Now, substitute this value of x into Equation 2:
3(30 - y) - 2y = 30
Simplify the equation:
90 - 3y - 2y = 30
90 - 5y = 30
Subtract 90 from both sides:
-5y = 30 - 90
-5y = -60
Divide both sides by -5:
y = -60 / -5
y = 12
Now we have the value of y. Substitute this value into Equation 1 to find x:
x + 12 = 30
x = 30 - 12
x = 18
So, the two numbers are x = 18 and y = 12.
To find the product of the two numbers, we simply multiply them:
Product = x * y
Product = 18 * 12
Product = 216
Therefore, the product of the two numbers is 216.
I hope that helps! Let me know if you have any further questions.