Another one about the Systems of Linear Equations in two Variables?

Question

34. A woman has a certain amount of money invested. If she had $6000 more invested at a rate 1 percent lower, she would have the same yearly income from the investment. Furthermore, if she had $4500 less invested at a rate 1 percent higher, her, her yearly income from the investment would also be the same. How much does she have invested, and at what rate is it invested?

35. A chemist has two acid solutions. One contains 15 percent acid and the other contains 6 percent acid. How many cubic centimeters of each solution should be used to obtain 400cm3 of a solution that is 9 percent acid?

36. A tank contains a mixture of insect spray and water in which there are 5 gal of insect spray and 25 gal of water. A second tank also contains 5 gal of spray but only 15 gal of water. If it is desired to have 7.5 gal of a mixture of which 20 percent is spray, how many gallons should be taken from each tank?

Answer 1

This is a bit of a mixed bag

(34) I thought you said LINEAR equations. This is only linear if it is SIMPLE INTEREST

SI = PRT/100

= (P+6000)(R-1)T/100 = (P-4500)(R+1)T/100

eliminating T/100
Eq1... (P+6000)(R-1) = PR
Eq2... (P-4500)(R+1) = PR
Eq3... (P+6000)(R-1) = (P-4500)(R+1)

PR+6000R-P-6000 = PR ...Eq1. Expand brackets
6000R-P=6000

Similarly
PR-4500R+P-4500 = PR ...Eq2
P-4500R = 4500

So...
1500R = 10500
R = 10500/1500
R = 7

P = 4500+4500R
P = $36000

(35)
addition of x mL of first solution to y mL of second solution yields a solution that is

(15x + 6y)/(x+y) = 9

Total vol is 400mL so x + y = 400

15x + 6y = 3600
6x + 6y = 2400
9x = 1200
x = 133.333 mL

x = 133 and 1/3 mL

y = 400-133.333mL
= 266.667mL

y = 266 and 2/3 mL

(36) Use similar method to generate equations from the text