Question

Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles. Find the number of marbles Leah has.

Answer 1

Answer:

Leah has 48 marbles.

Step-by-step explanation:

Represent the number of marbles that each person has by L and D.

Leah has 28 more marbles than Dan:  L = D + 28.

Then (1/3)L = (4/5)D.  Here the LCD is 15, and so multiplying this equation by 15 will remove the fractions:  15(1/3)L = 15(4/5)D.  

Therefore, 5L = 12D, and D = 5L/12.

Then, since L = D + 28,        L = (5/12)L + 28, or

12L = 5L + 336, or

7L = 336, or

L = 336/7 = 48.

Leah has 48 marbles.  That means that Dan has 20 marbles.

Answer 2

The number of marbles Leah has is 48 and Dan is 20 if Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles.

Let x be the number of marbles Leah has.

Let y be the number of marbles Dan has.

Leah has 28 more marbles than Dan:  

x = y + 28

(1/3)x = (4/5)y

Solving above two linear equation, we get:

5x = 12y

5(y + 28) = 12y

5y + 140 = 12y

12y - 5y = 140

7y = 140

y = 140/7 = 20

x = 20 + 28 = 48

Thus, the number of marbles Leah has is 48 and Dan is 20 if Leah has 28 more marbles than Dan. 1/3 of Leah’s marbles is equal to 4/5 of Dan’s marbles.

Learn more about the linear equation here:

brainly.com/question/11897796

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