Terence is looking for two numbers. If he multiplies the first number by three and adds one, he gets the second number. However, the first number is only 1/4 of the second number. What are the two numbers?
3n+1 = m
n = m/4
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3(m/4) +1 = m
3 m + 4 = 4 m
m = 4
n = 1
To find the two numbers, let's assume the first number as "x" and the second number as "y".
According to the given information, if Terence multiplies the first number by three and adds one, he gets the second number. So we can represent this as an equation: 3x + 1 = y.
The second piece of information states that the first number is only 1/4 of the second number. Mathematically, this is written as: x = (1/4) * y.
Now we can solve these two equations simultaneously to find the values of x and y.
To start, let's substitute the value of y from the second equation into the first equation:
3x + 1 = (1/4) * y
Since x = (1/4) * y, we can replace x with (1/4) * y in the first equation:
3 * (1/4) * y + 1 = y
Simplifying this equation, we get:
(3/4) * y + 1 = y
To get rid of the fractions, we can multiply the entire equation by 4 to eliminate the denominators:
4 * [(3/4) * y + 1] = 4 * y
After simplifying this equation, we have:
3y + 4 = 4y
Now, subtract 3y from both sides of the equation:
4 - 3y = y
Next, subtract 4 from both sides of the equation:
-3y = y - 4
Now, add 3y to both sides of the equation:
0 = 4y + 4
Finally, subtract 4 from both sides of the equation:
-4 = 4y
Now divide both sides of the equation by 4:
y = -1
So, we have found the value of y, which is -1.
Since x = (1/4) * y, we can substitute the value of y into the equation to find x:
x = (1/4) * (-1)
x = -1/4
Therefore, the two numbers are x = -1/4 and y = -1.