Three times the difference of two numbers is 3 more than the larger and three times their sum is less than 8 Times the smaller by 2 .find the numbers
smaller --- x
larger --- y
Now just translate into Math.
3(y - x) = y+3
3y - 3x = y+3
3x - 2y = -3 **
3(y+x) = 8x + 2
3y + 3x = 8x + 2
5x - 3y = 2 ***
solve ** and ***
You should get two whole numbers.
To solve this problem, let's assign variables to the two numbers. Let's say the larger number is represented by "x" and the smaller number is represented by "y."
According to the problem, three times the difference of the two numbers is 3 more than the larger number. We can write this as an equation:
3(x - y) = x + 3
Additionally, we are given that three times their sum is less than 8 times the smaller number by 2:
3(x + y) = 8y - 2
Now we have a system of two equations. Let's solve it:
From the first equation:
3x - 3y = x + 3
2x - 3y = 3
From the second equation:
3x + 3y = 8y - 2
3x - 8y = -2
Now we have a system of two equations with two variables. We can solve it using any method, but let's use the method of substitution:
From the first equation:
2x - 3y = 3
2x = 3 + 3y
x = (3 + 3y) / 2
Substitute this value of x into the second equation:
3( (3 + 3y) / 2 ) - 8y = -2
(9 + 9y) / 2 - 8y = -2
9 + 9y - 16y = -4
-7y = -13
y = 13/7
Now substitute the value of y back into the expression for x:
x = (3 + 3(13/7)) / 2
x = (3 + 39/7) / 2
x = 24/7
Therefore, the two numbers are approximately x = 24/7 and y = 13/7.