Word probs: number polled / shares purchased

[Kristen_Opp]

The algebra on these problems is easy but I'm having trouble getting them set up correctly!?!

1. A group of people were polled and 20% of them, or 700 were in favor of the new product over the best selling brand. how many people were polled?

So I know it's asking: 20% of what number equals 700... and the answer to that is 3500.. but my teacher wants me to show work and I can't cause I figured it out by taking 20% of 100 which is 20 and then comparing the difference between 20 and 700 and X's the difference by 100 (I know that's weird but I do it in my head) so now I need to write it out in legitimate algebra form. : ) help!

2. An investment club bought a bond of an oil corp for $5000. The bond yields 8% per year. the club now wants to buy shares of stock in a hospital supply company. The stock sells at $20 per share and earns a dividend of $.50 per share a year. how many shares should the club buy so that its total investment in stocks and bonds yields 5% per year?

(this problem is like a more complicated version of the first one but it's too big for me to outsmart I just would like to know how to set it up in an equation and then I can take it from there. Thanks

 

[Mrspi]

Re: Word problem difficulty

The algebra on these problems is easy but I'm having trouble getting them set up correctly!?!

1. A group of people were polled and 20% of them, or 700 were in favor of the new product over the best selling brand. how many people were polled? So I know it's asking: 20% of what number equals 700... and the answer to that is 3500.. but my teacher wants me to show work and I can't cause I figured it out by taking 20% of 100 which is 20 and then comparing the difference between 20 and 700 and X's the difference by 100 (I know that's weird but I do it in my head) so now I need to write it out in legitimate algebra form. : ) help!

Why not just turn your "method" into an equation?
Let x = total number polled

20/100 = 700/x

2. second questions:
an investment club bought a bond of an oil corp for $5000. The bond yields 8% per year. the club now wants to buy shares of stock in a hospital supply company. The stock sells at $20 per share and earns a dividend of $.50 per share a year. how many shares should the club buy so that its total investment in stocks and bonds yields 5% per year?
(this problem is like a more complicated version of the first one but it's too big for me to outsmart I just would like to know how to set it up in an equation and then I can take it from there. Thanks

Let x = number of shares of stock purchased
20x = dollars invested in stock
.5x = dividends earned on stock


5000 = dollars invested in bond
0.08(5000) = interest earned in 1 year on bonds

5000 + 20x = total amount invested
.05(5000 + 20x) = interest earned in 1 year on total investment at 5%

Ok....here's the basis for your equation:

dividends on stock + interest on bond = total investment income

.5x + .08(5000) = .05(5000 + 20x)