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Mr. Lim, Mr. Bell, and Mrs. Walker paid for a meal.

- Mr. Lim paid \(\frac{1}{5}\) of the amount Mr. Bell and Mrs. Walker paid together.
- Mr. Bell paid \(\frac{1}{4}\) of the amount Mr. Lim and Mrs. Walker paid.

A) What fraction of the total cost of the meal did Mrs. Walker pay?

Answer :

As a result, Mrs. Walker contributed a portion of the overall cost of the supper, which is: 400/61 - (16B + 25L) / (61C) (61C)

what is fraction ?

A fraction is a number that in mathematics represents a portion of a whole. It consists of a horizontal line between the numerator and denominator of two numbers. The denominator is the total number of equally sized components that make up the whole, whereas the numerator is the number of parts that are being taken into account. As an illustration, the fraction 3/4 denotes three of the four equal pieces. The denominator, 4, indicates that the entire is divided into four equal parts, while the numerator, 3, indicates that three parts are being taken into consideration.

given

Payment to Mr. Lim:

1/5(B + W) = (B + W)/5

Payment to Mr. Bell:

1/4(L + W) = (L + W)/4

These equations can be combined to find the value of W, or the amount Mrs. Walker paid:

(L + W)/4 + W + (B + W)/5 = C

To get rid of the fractions, multiply both sides by 20, which is the least common multiple of 5 and 4. This gives us:

20W + 4(B + W) + 5(L + W) = 20C

By enlarging and condensing, we obtain:

20C = 4B + 4W + 5L + 5W + 20W

9W + 4B + 5L = 20C

Now, we may change the expressions for the payments made to Mr. Lim and Mr. Bell to:

9W plus 4 (1/5 B + W) plus 5 (1/4 L + W) equals 20C.

If we simplify, we get:

9W + 4B + 4W + 4W + 4W + 5L + 5W = 20C.

When we multiply both sides by 20 to once more get rid of the fractions, we get:

400C = 180W + 16B + 16W + 25L + 25W

20C = 4B + 4W + 5L + 5W + 20W

9W + 4B + 5L = 20C

Now, we may change the expressions for the payments made to Mr. Lim

If we simplify, we get:

61W + 16B + 25L = 400C

We may now determine W:

W = (400C - 16B - 25L) / 61

We can divide W by the overall cost C to determine the portion of the cost of the lunch that Mrs. Walker covered:

W/C = (400C - 16B - 25L) / (61C)

W/C = 400/61 - (16B + 25L) / (simplified) (61C)

As a result, Mrs. Walker contributed a portion of the overall cost of the supper, which is: 400/61 - (16B + 25L) / (61C) (61C) .

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