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VLD [36.1K]
3 years ago
10

What is the difference between finding the greatest common factor and the least common multiple of the numbers 4 and 12?

Mathematics
1 answer:
dangina [55]3 years ago
8 0

Answer: The difference is factor is a circumstance, fact, or influence that contributes to a result or outcome. and multiple is A multiple of a number is that number multiplied by an integer.


Step-by-step explanation:


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Ms. Nina has 10 lbs of 25% sugar syrup. How much water does she need to add to make 10% sugar syrup?
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She has 10lbs of 25% syrup... so, in the 10lbs, 25% of that is syrup, the rest, namely the 75% remaining is water or other substances.

let's say she adds "x" lbs of water, to get "y" lbs for the 10% mixture.

how much is 25% of 10lbs?  well, (25/100) * 10, or 2.5.

the water has no sugar syrup in it, so is just pure water, so the amoun of syrup in it is 0%, how much is 0% of "x" lbs?  well, (0/100) * x, or 0.00x, which is just 0.

how much is 10% of "y" lbs?  well (10/100) * y, or 0.10y.

whatever "x" and "y" are, we know that 10 + x = y.

we also know that the syrup amount in that is also 2.5 + 0.00x = 0.10y, thus


\bf \begin{array}{lccclll}&#10;&\stackrel{lbs}{syrup}&\stackrel{concentration~\%}{syrup}&\stackrel{concentration}{amount}\\&#10;&------&------&------\\&#10;\textit{25\% syrup}&10&0.25&2.5\\&#10;\textit{pur water}&x&0.00&0.00x\\&#10;------&------&------&------\\&#10;\textit{10\% mixture}&y&0.10&0.10y&#10;\end{array}&#10;\\\\\\&#10;\begin{cases}&#10;10+x=\boxed{y}\\&#10;2.5+0.00x=0.10y\\&#10;----------\\&#10;2.5 = 0.10\left( \boxed{10+x} \right)&#10;\end{cases}&#10;\\\\\\&#10;2.5=1 + 0.10x\implies 1.5=0.10x&#10;\\\\\\&#10;\cfrac{1.5}{0.10}=x\implies 15=x
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