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Answer:
Linda makes 3 more cards than Paul.
Step-by-step explanation:
Let's express the affirmations into equations:
Paul (P) can make 1 card for every 3 cards Linda (L) makes:
[tex] \frac{P}{L} = \frac{1}{3} [/tex]
[tex] 3P = 1L [/tex] (1)
Linda can make 3 cards for every 2 cards that Aaron (A) makes:
[tex] \frac{L}{A} = \frac{3}{2} [/tex]
[tex] 2L = 3A [/tex] (2)
During a week, Aaron makes 72 cards, hence the number of cards of Linda and Paul can be calculated as follows:
From equation (2):
[tex] L = \frac{3}{2}A = \frac{3}{2}72 = 108 [/tex]
Now, from equation (1):
[tex] P = \frac{1}{3}L = \frac{1}{3}108 = 36 [/tex]
Finally, the number of cards that Linda makes more than Paul is:
[tex] \frac{L}{P} = \frac{108}{36} = 3 [/tex]
Therefore, Linda makes 3 more cards than Paul.
I hope it helps you!
Number of more cards Linda made than Paul for the week is; she made 72 more cards than Paul for the week.
We are told that;
Paul can make 1 card for every 3 cards Linda makes. Let number of card Paul makes be p and let number of cards Linda makes be L. Thus, we have;
p/l = 1/3
Thus;
l = 3p
Linda can make 3 cards for every 2 cards that Aaron makes. If number of cards that Aaron makes is a, then;
l/a = 3/2
l = 3a/2
Now, we are told that Aaron made 72 cards in a week. Thus, a = 72 and so we have;
l = (3 × 72)/2
l = 108 cards for the week
Since l = 3p, then;
p = l/3
p = 108/3
p = 36 cards for the week.
Thus;
Difference between number of Linda's cards and Paul's cards = 108 - 36 = 72
Thus,linda made 72 more cards than Paul for the week.
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