Functions and Elimination/substitution w/ word problems

Question

3. John invested $10,000 between 2 different stocks. One stock yielded a 10% return and the other 5% return. How much is invested in each stock if his total return is $650?

11. Bob invested in 2 businesses. He gained 10% on the first investment and 12% in the second. If he invested $1,000 more in the first business and gained a total of $6,040, how much money did he invest in each business?

21. A bronze alloy containing 8% zinc is mixed with another alloy containing 12% zinc to get 900 lb of bronze alloy containing 9.5% zinc. How much of each alloy is used?

The function C(x) = 1.19x + 7.5 represents the cost of producing x stainless steel widgets. R(x) = 1.69x represents the revenue from selling x of them. Find the following.

26. Number that must be sold to break even.

27. Profit from selling 500

28. Profit or loss from selling 200 at regular price and 300 at half price.

thank you so much!!

Answer 1

a + b = 10,000

0.1a + 0.05b = 650

First, we solve the 1st equation for either variable. I'll do a. I'm also going to multiply the 2nd equation by 100 to get rid of the pesky decimals.

a = 10,000 - b

10a + 5b = 65,000

OK, since a equals something, we can substitute that something where we see a.

10(10,000 - b) + 5b = 65,000

100,000 - 10b + 5b = 65,000

-5b = -35,000

b = $7000

a = 10,000 - 7000

a = $3000

I bet you can get the rest.