# Phyllis invested \$12,000, a portion earning a simple interest rate of 4 1/2% per year and the rest earning a rate of 4% per year.After 1 year the total interest earned on these investments was \$525.How much money did she invest at each rate ?

2
by euricahacosta

2014-09-28T21:58:33+08:00
Let 'x' be the amount invested at 4.5%
'y' be the amount invested at 4%
Since you are provided that the total investments earned 525 then you'll have the equation as:
0.045x + 0.04y = 525   -----equation 1
You're given the total amount of 12,000 then
x + y = 12,000     -------equation 2
transposing x to the right side for equation 2
y = 12,000 - x   ---------equation 3
substitute equation 3 to equation 1
0.045x + 0.04y = 525
0.045x + 0.04(12,000-x) = 525
0.045x + 480 - 0.04x = 525
0.045x - 0.04x = 525 - 480
0.005x = 45
x = 9,000
substitute the value of 'x' to equation 3
y = 12,000 - x
y = 12,000 - 9,000
y = 3,000
2014-09-28T22:10:49+08:00
Let  be the amount invested at 4.5%.
y be the amount invested at 4%.

Since you are provided that the total investments earned 525, then you'll have the equation as:
0.045x + 0.04y = 525
Total amount of 12,000 then:
x + y = 12,000
Transpose x to the right side:
y = 12,000 - x
Substitute equation 3 to equation 1
0.045x + 0.04y = 525
0.045x + 0.04(12,000-x) = 525
0.045x + 480 - 0.04x = 525
0.045x - 0.04x = 525 - 480
0.005x = 45
x = 9,000
Substitute the value of x to equation 3:
y = 12,000 - x
y = 12,000 - 9,000
y = 3,000