can someone help me solve this? not just an answer but a method of solving cause im having a hard time grasping this.
Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. Find the numbers.
3xy = 4y
x+y = 21
let x equal the larger number
let y equal the smaller number
ok..
take it step by step. u first divide 4y on both sides. if that doesn't work, just plug numbers in. hope this helps! please answer my question! thanks.
XOXO
Hazel
Three times the larger of two numbers is equal to four times the smaller. Let x equal the larger number, and
let y equal the smaller number.
3x = 4y or dividing both sides by 4, y = 3/4x
The sum of the numbers is 21.
x + y = 21
Substitute 3/4x for y in the second equation. and solve for x. Put that value into the first equation to find y. Check by putting both values into the second equation.
I hope this helps a little more. Thanks for asking.
Sure, I can help you with that! To solve this problem, we will use a method called "system of equations".
Let's assign variables to the two numbers. Let's call the larger number "x" and the smaller number "y".
According to the problem, three times the larger number is equal to four times the smaller number. This can be written as:
3x = 4y (Equation 1)
The problem also tells us that the sum of the two numbers is 21:
x + y = 21 (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of x and y.
To eliminate one variable, let's multiply Equation 2 by 3, so that the coefficient of x in both equations is the same (3x):
3(x + y) = 3(21)
3x + 3y = 63 (Equation 3)
Now we can substitute Equation 3 into Equation 1:
4y = 3x
3x + 3y = 63
Rearranging Equation 3, we get:
3y = 63 - 3x
Substituting this into Equation 1:
4(63 - 3x) = 3x
Expand the equation:
252 - 12x = 3x
Bring the terms with x to one side:
252 = 15x
Now, we can solve for x by dividing both sides by 15:
x = 252 / 15
x = 16.8
Since x represents the larger number, it cannot be a decimal. So, let's round it to the nearest whole number:
x ≈ 17
Now, substitute the value of x back into Equation 2 to find y:
17 + y = 21
Rearranging the equation, we can solve for y:
y = 21 - 17
y = 4
So the two numbers are x = 17 and y = 4.
To check if the solution is correct, substitute these values back into the original equations:
3x = 4y
3(17) = 4(4)
51 = 51
x + y = 21
17 + 4 = 21
Both equations are satisfied, so the solution is correct. The two numbers are 17 and 4.