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The second system of equations,
is correct.
We know that Bethany's age is x. Since Laura is 13 years older, her age is x+13. The product of their ages is equal to twice Amanda's age, and Amanda's age is y. This gives us:
x(x+13) = 2y
Using the distributive property, we have
x²+13x=2y
Dividing everything by 2 (to isolate y), we have:
x²/2 + (13/2)x = y
If we take 20 years off of Bethany's age, it is now represented as x-20. Taking 20 years off of Laura's age would be (x+13-20) or x-7. The product of their ages now is equal to David's age; David is 11 years older than Amanda, so his age is y+11. This gives us:
(x-20)(x-7)=y+11
Multiplying the binomials we have:"
x*x - 7*x - 20*x - 20(-7) = y+11
x²-7x-20x--140=y+11
x²-27x+140=y+11
To isolate y, subtract 11 from both sides:
x²-27x+140-11 = y+11-11
x²-27x+129 = y
is correct.
We know that Bethany's age is x. Since Laura is 13 years older, her age is x+13. The product of their ages is equal to twice Amanda's age, and Amanda's age is y. This gives us:
x(x+13) = 2y
Using the distributive property, we have
x²+13x=2y
Dividing everything by 2 (to isolate y), we have:
x²/2 + (13/2)x = y
If we take 20 years off of Bethany's age, it is now represented as x-20. Taking 20 years off of Laura's age would be (x+13-20) or x-7. The product of their ages now is equal to David's age; David is 11 years older than Amanda, so his age is y+11. This gives us:
(x-20)(x-7)=y+11
Multiplying the binomials we have:"
x*x - 7*x - 20*x - 20(-7) = y+11
x²-7x-20x--140=y+11
x²-27x+140=y+11
To isolate y, subtract 11 from both sides:
x²-27x+140-11 = y+11-11
x²-27x+129 = y