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# math problem

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A department store gives away a \$10 gift card to every 20th customer and a \$15 gift card to every 45th customer. Which customer will be the first to recieve both gift cards after this customer receives both gift cards what is the total amount in gift cards the store has given away

Sep 1, 2020

#1
+1

The LCM(20, 45) = 180

So, it will be the 180th customer who will receive both gift cards.

180 / 20 = 9 - \$10 gift cards were given away

180 / 45 = 4 - \$15 gift cards were given away

[9  x \$10] + (4 x \$15] =\$90 + \$60 =\$150 worth of gift cards were given away in that period of 180 days.

Sep 1, 2020
#2
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When the customer recieves both gift cards (i wish i were that guy! who doesn't like free money?), it would be the LCM of 20 and 45. Then we could do some math, and voila! the answer

LCM (20, 45)

How to do this? Let's go back to what we learned in third grade: GCF and LCM (or was it fourth? it has been such a long time...)

This one isn't hard: we don't need to use the "prime factorization method", we can use the "list out the numbers" method we learned:

20: 20, 40, 60, 80, 100, 120, 140, 160, 180

45: 45, 90, 135, 180

So, now we know that the 180th customer got 2 gift cards

But we are not done yet! We need to know how many people have recieved the gift card!

There are 9 \$10 (90 total) gift cards, and \$15 (60 total) gift cards, so add that together, and we have a total of \$150 worth of gift cards.

1. 180th person

2. \$150 worth of gift cards

:)

Sep 1, 2020
edited by ilorty  Sep 1, 2020
edited by ilorty  Sep 1, 2020