Bella0417
Bella0417 Bella0417
  • 23-05-2017
  • Mathematics
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One number is 7 more than another. The difference between their squares is 161. What are the numbers?

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jdoe0001 jdoe0001
  • 23-05-2017
let's say the numbers are "a" and "b"

now, we know one of them is 7 more than the other, so hmmm let's say "b" is 7 more than "a", so b = a + 7

the difference of their squares is 161, alrite

[tex]\bf a^2-b^2=161\qquad b=a+7\implies a^2-(a+7)^2=161 \\\\\\ a^2-(a^2+14a+49)=161\implies \underline{a^2-a^2}-14a-49=161 \\\\\\ -14a-49=161\implies -49-161=14a\implies -210=14a \\\\\\ \cfrac{-210}{14}=a[/tex]

and surey you know how much that is

now, what's "b"? well, b = a + 7
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