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Harrizon [31]
3 years ago
15

The owner of a small store buys coats for ​$60.00 each. He sells the coats for ​$96.00 each. What percent of the purchase price

is the sale​ price?
Mathematics
1 answer:
Sliva [168]3 years ago
3 0

The sale price of the coats is 160% of the purchase price of the coats.

<u>Step-by-step explanation:</u>

The owner buys the coats at a purchase price= $60

He sells the coats for a selling price= $96

Now, the question is:

The selling price $96 is what percentage of the purchase price $60

<u>step 1</u>: 96= x% of 60

<u>step 2</u>: 96= (x/100)*60

<u>step 3</u>: 96= 6x/10

<u>step 4</u>: 960/6 = x

<u>step 5</u>: x = 160%

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How many positive integers $n$ from 1 to 5000 satisfy the congruence $n \equiv 5 \pmod{12}$?
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The equivalence n \equiv 5 \pmod{12}

means that n-5 is a multiple of 12.

that is

n-5=12k, for some integer k

and so

n=12k+5


for k=-1, n=-12+5=-7

for k= 0, n=0+5=5 (the first positive integer n, is for k=0)


we solve 5000=12k+5 to find the last k

12k=5000-5=4995

k=4995/12=416.25

so check k = 415, 416, 417 to be sure we have the right k:

n=12k+5=12*415+5=4985

n=12k+5=12*416+5=4997

n=12k+5=12*417+5=5009


The last k which produces n<5000 is 416


For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,

thus there are 417 integers n satisfying the congruence.


Answer: 417

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Step-by-step explanation:

<h3><u>some relevant limit laws</u></h3>

lim C = C where c is a constant.

lim( f(x)  + g(x)) =lim f(x) + lim g(x)

lim( f(x)g(x)) =lim f(x) * lim g(x)

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