alg 2 help plz?

Question

1. Anoa bought two plots of land for total of $120000. when she sold the first plot, she made a profit of 15%. When she sold the second, she lost 10%. her total profit was $5500. how much did she pay for each piece of land?
2. a church building fund has invested some money in two ways: part of the money at 4% interest and four times as much at 3.5%. find the amount invested at each rate if the total annual income from interest is $36003.
3. Latasha Williams earned $48000 from royalties on her cookbook. she paid a 28% income tax on these royalties. the balance was invested in two ways, some of it at 3.25% interest and some at 1.75%. the investments produced $904.80 interest per year. find the amount invested at each rate.

Answer 1

1. Anoa bought two plots of land for total of $120000. when she sold the first plot, she made a profit of 15%. When she sold the second, she lost 10%. her total profit was $5500. how much did she pay for each piece of land?

Set up 2 formulas. x and y will be the price paid initially for the 2 plots.
x + y = $120000
.15x - .10y = 5500

Define y in terms of x:
y = $120000 - x

Plug y into formula 2:
.15x - .10 ($120000 - x) = $5500
.15x + .10x - $12,000 = 5500
.25x = $17,500
x = $70,000 (solution!)
y = 120,000 - 70,000 = $50,000 (solution!)

Check:
.15 * 70,000 - .10 * 50,000 = 5500
10500 - 5000 = 5500
5500 = 5500 (check!)