Pg 220 # 59 Is this answer given correct for the following question?If it is not correct what is the appropriate answer

Question: A quantity and its two-thirds and its half and its one-seventh together make 33. Find the quantity

Answer: 14+ ¼ + 1/56 + 1/97 + 1/194 + 1/388 + 1/679 + 1/776

If you are seekng the number X whose 2/3rds, 1/2, and 1/7th, when added to itself = 33, then

X + 2X/3 + X/2 + X/7 = 33

Clear the denominator and you will have X.

To determine if the given answer is correct for the question on page 220, number 59, we first need to understand the problem. The question states that a quantity and its two-thirds and its half and its one-seventh together make 33. We're asked to find the quantity.

To solve this problem, we can break it down into steps:

1. Let's assume the quantity we're looking for is "x."
2. According to the problem, the two-thirds of the quantity is (2/3)x, the half of the quantity is (1/2)x, and the one-seventh of the quantity is (1/7)x.
3. The question states that when we add these values together, it equals 33.
So, the equation we can form is:

x + (2/3)x + (1/2)x + (1/7)x = 33

To simplify this equation, we need to find a common denominator for the fractions involved.

4. The common denominator for 3, 2, and 7 is 42. So, we can rewrite the equation as:

(42/42)x + (28/42)x + (21/42)x + (6/42)x = 33

Simplifying further:

(97/42)x = 33

5. To solve for x, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of (97/42):

x = 33 * (42/97)

Now, let's calculate the value of x:

x = 14 * (42/97)
= (14 * 42) / 97
= 588 / 97

So, the appropriate answer for the quantity is 588/97.

Comparing this with the given answer of "14 + ¼ + 1/56 + 1/97 + 1/194 + 1/388 + 1/679 + 1/776," we can see that it is not correct. The correct answer is 588/97.