Luz and Cathy were both given the same amount of money by their father. Luz spent 3/4 of her money while Cathy spent 5/7 of hers. Who spent more money?
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Luz and Cathy were both given the same amount of money by their father. Luz spent 3/4 of her money while Cathy spent 5/7 of hers. Who spent more money?
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Answer:
Step-by-step explanation:
To compare Luz and Cathy's spending, we need to find the total amount of money each of them spent.
Let `L` be the total amount of money Luz received from her father, and `C` be the total amount of money Cathy received from her father.
We know that Luz spent 3/4 of her money, or `0.75L`, while Cathy spent 5/7 of her money, or `0.71428571C`.
To find who spent more money, we can compare `0.75L` and `0.71428571C`.
Since `0.75L > 0.71428571C`, we can conclude that Luz spent more money than Cathy.
In other words, `0.75L > 0.71428571C`.
Answer:
To determine who spent more money, we need to compare the fractions of money spent by Luz and Cathy.
Luz spent 3/4 of her money.
Cathy spent 5/7 of her money.
To make a comparison, we can find a common denominator for the fractions. The least common multiple of 4 and 7 is 28.
Now, let's find equivalent fractions with a common denominator of 28:
Luz: (3/4) x (7/7) = 21/28
Cathy: (5/7) x (4/4) = 20/28
Comparing the two fractions, Luz spent 21/28 of her money, and Cathy spent 20/28 of her money. Since 21/28 is greater than 20/28, Luz spent more money than Cathy.