# Thread: Solving and Simplifying Equations

1. ## Solving and Simplifying Equations

From the first-degree equations section of my pre-calc book:

1) (8)/(3k-9) - (5)/(k-3) = 4

2) Jason bought two plots of land for a total of $120,000. On the first plot he made a profit of 15%. On the second, he lost 10%. His total profit was$5500. How much did he pay for each piece of land?

Thanks!

2. $\frac{8}{3k-9} - \frac{5}{k-3} = 4$

$\frac{8}{3(k-3)} - \frac{5}{k-3} = 4$

Now mulitply both sides through by k-3

$\frac{8}{3} - 5 = 4(k-3)$

Can you solve it from here?

3. Originally Posted by NRS11

2) Jason bought two plots of land for a total of $120,000. On the first plot he made a profit of 15%. On the second, he lost 10%. His total profit was$5500. How much did he pay for each piece of land?

Thanks!
Let X be the value of lot 1 and Let Y be the value of Lot 2

So $X + Y = 120,000$

Also $1.15X + 0.9Y = 120,000 + 5,500$

We now have 2 functions with 2 variables, can you solve this?

4. PROBLEM: "Jason bought two plots of land for a total of $120,000. On the first plot he made a profit of 15%. On the second, he lost 10%. His total profit was$5500. How much did he pay for each piece of land?"

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Solution:

Let x = amount of the first lot

120,000 - x = amount of the second lot

(15%)x - 10%(120,000 - x) = 5,500,

0.15x - 12,000 + 0.10x = 5,500,

0.25x = 5,500 + 12,000,

x = (5,500 + 12,000)/0.25 = 70,000 - first lot,

120,000 - x = 120,000 - 70,000 = 50,000 - 2nd lot

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5. Alright, thanks so much... seeing each step was really helpful.