I'm stuck on my math homework. Need help! Please solve!

Answers:

Explanation:

s = Sam's age right now

2s = the mother's age right now, since she is twice as old as Sam currently.

In 12 years time, Sam will be s+12 years old.

12 years ago from this current year, the mother was 2s-12 years old.

Since we're told these future and past ages line up, this means s+12 and 2s-12 are the same value

Set the expressions equal to one another and solve for s.

s+12 = 2s-12

s-2s = -12-12

-s = -24

s = 24

Sam is currently 24 years old.

His mother is currently 2s = 2*24 = 48 years old.

12 years ago, his mother was 2s-12 = 48-12 = 36 years old.

12 years from now, Sam will be s+12 = 24+12 = 36 years old.

Since we get 36 each time, this confirms we have the correct answers.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

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step-by-step explanation: