Answer: Unlock code = 76
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Explanation:
Use a factor tree to find the prime factorization of each value
22 = 2*11
30 = 2*3*5
Both values have '2' in common and this is the largest such value. Therefore, the GCF of 22 and 30 is 2.
So E = 2
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Since 3 and 8 have no factors in common (other than 1), this means the LCM is 3*8 = 24
We can say that F = 24.
If the numbers had some larger number in common, then we'd have to do a bit more work to find the LCM.
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As the hint suggests, we'll use the distributive property to show that
3*(7+10) = G + 30
3*7 + 3*10 = G + 30
21 + 30 = G + 30
21 = G .... subtract 30 from both sides; they cancel and go away
G = 21
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Use the same idea for the other equation as well
5*(3 + H) = 15 + 45
5*3 + 5*H = 15 + 45
15 + 5H = 45
5H = 45 ............ subtract 15 from both sides; they go away
H = 45/5 ......... divide both sides by 5
H = 9
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The unlock code is
E+F+G+H = 2+24+21+29 = 76
