One number is 3 more than another if four times the larger is divided by the smaller the quotient is 2. FIND THE TWO NUMBERS
smaller ---- x
larger ------ x+3
4(x+3)/x = 2
4x + 12 = 2x
carry on
To solve this problem, let's set up two equations based on the given information.
Let's say the smaller number is x and the larger number is y.
From the first statement "One number is 3 more than another," we can write the equation:
y = x + 3
From the second statement "Four times the larger is divided by the smaller and the quotient is 2," we can write the equation:
4y / x = 2
Now, we have a system of two equations. We can solve them simultaneously to find the values of x and y.
Substituting the first equation into the second equation, we have:
4(x + 3) / x = 2
Now, let's simplify the equation:
4(x + 3) = 2x
Expanding the brackets:
4x + 12 = 2x
Bringing all the terms to one side:
4x - 2x = -12
Simplifying:
2x = -12
Divide both sides by 2:
x = -6
Now, substitute the value of x back into the first equation to find the value of y:
y = x + 3
y = -6 + 3
y = -3
So, the two numbers are -6 and -3.