Answer:
$2,000 was invested at 15% rate.
$3,000 was invested at 16% rate.
Step-by-step explanation:
Carolyn received a check last week.
She invested part at 15% and;
$1000 more than this amount at 16%
She will earn simple interest of $780 in one year.
Simple interest formula is;
I = PRT
Where I is the interest, P is the amount invested, R is the rate and T is the time.
Lets say the part invested at 15% rate was $x
Interest earned here = $x × [tex]\frac{15}{100}[/tex] × 1 = $0.15x
The amount invested at 16% was $x + $1000
Interest earned here = ($x + $1000) × [tex]\frac{16}{100}[/tex] × 1 = $0.16x + $160
Total interest earned is equal to:
$0.15x + $0.16x + $160 = $780
$0.31x = $780 - $160 = $620
$x = $620 ÷ 0.31 = $2000
So the amount invested at 15% rate was $2000 and;
The amount invested at 16% rate was $2000 + $1000 = $3000
