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3 years ago

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.

Mathematics

2 answers:

konstantin123 [22]3 years ago

7 0

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.

Gnoma [55]3 years ago

3 0

X= Leah
Y= Dan
Make a system of equations
Y=X-28
1/3X=4/5Y
Then input X-28 for Y
1/3X=4/5(X-28)
Now solve for X
X=48

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