Phyllis invested 6500065000 dollars, a portion earning a simple interest rate of 55 percent per year and the rest earning a rate of 77 percent per year. After one year the total interest earned on these investments was 39303930 dollars. How much money did she invest at each rate?
A) At rate 55 percent
B) At rate 77 percent

Let x represent amount invested at 5% and y represent amount invested at 7%.  

We have been given that Phyllis invested 65000, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 7 percent per year. We can represent this information in an equation as:

We are also told that after one year the total interest earned on these investments was $3930. We can represent this information in an equation as:

Upon substituting equation (1) in equation (2), we will get:

Therefore, Phyllis invested $31,000 at 5%.

Upon substituting in equation (1), we will get:

Therefore, Phyllis invested $34,000 at 7%.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer