Lucy is supposed to subtract a certain number from 48 and divide the result by the same number. However, she divided 48 by the same number and subtracted the number from the quotient giving an answer of two. What should be the correct answer?
What she was told to do:
(x-48)/x
what she did:
48/x - x = 2
solve for x, then plug into "what she was told to do"
btw, there are two values of x.
my prob is how to find x in the equation
48/x - x = 2
my answer is 6 but i dont know the process of arriving
48/x - x = 2
multiply each term by x to get the quadratic
48 - x^2 = 2x
x^2 + 2x - 48 = 0
(x - 6)(x + 8) = 0
x = 6 or x = -8
btw, What she was told to do should have been:
(48-x)/x
if x = 6,
(48-x)/x = (48-6)/6 = 7
if x = -8,
(48-x)/x = (48 + 8)/-8 = -7
To find the correct answer, we need to solve the given problem step by step.
Let's break down the problem using variables:
Let's say the number that Lucy was supposed to subtract and divide by is 'x'.
According to the problem:
1. Lucy was supposed to subtract 'x' from 48: 48 - x.
2. Then, she was supposed to divide the result by 'x': (48 - x) / x.
However, Lucy made a mistake and did the following steps instead:
1. Lucy divided 48 by 'x': 48 / x.
2. She then subtracted 'x' from the quotient: (48 / x) - x.
The given result is 2: (48 / x) - x = 2.
Now, let's solve the equation to find the correct answer:
(48 / x) - x = 2.
To simplify the equation, let's get rid of the fraction by multiplying through by 'x':
48 - x^2 = 2x.
Rearranging the equation, we have:
x^2 + 2x - 48 = 0.
Now, we can solve this quadratic equation to find the correct value of 'x'.
Factoring the quadratic equation gives us:
(x + 8)(x - 6) = 0.
Setting each factor equal to zero:
x + 8 = 0, which gives x = -8.
x - 6 = 0, which gives x = 6.
Since 'x' cannot be negative (division by zero), the correct value for 'x' is 6.
Therefore, the correct answer is:
(48 - x) / x = (48 - 6) / 6 = 42 / 6 = 7.