<h3>
Answers: 48 and 72</h3>
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Explanation:
The number 12 is a multiple of 3 because 3*4 = 12.
So when looking for common multiples of 3 and 12, we simply need to look at multiples of 12.
The multiples of 12 are:
- 12, 24, 36, 48, 60, 72, 84, 96, 120, ...
We see that 48 and 72 are on the list. The values 21, 27, 63, 81 are not on the list, so cross them out.
Now we could keep that list of multiples going to see if 844 is on there or not. A better method is to divide 844 over 12. If we get a whole number, then it's a multiple of 12.
844/12 = 70.333 approximately.
This shows that 844 is <u>not</u> a multiple of 12. So we cross 844 from the list.
Only 48 and 72 are multiples of 12 (and also multiples of 3).
The equation that could John solve to find w, the greatest width in centimeters he can use for the mosaic is option B: w(w + 2) = 48.
<h3>What is a system of equations?</h3>
A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The mosaic to be formed is rectangular in shape.
Area of a rectangle = length x width
The length is longer than the width by 2,
So, length = w+2
Area of a rectangle = (w+2) x w
The correct equation is B: w(w + 2) = 48
Learn more about equations here;
brainly.com/question/10413253
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