Question 1034821
Nicole invested a certain amount of money for one year and earned $78 in interest. Jon invested $260 more at an interest rate that was 1% less than Nicole, but earned the same amount of interest. Find Nicole's principal and interest rate. 
:
let n = amt invested by N
J invested $260 more, therefore
(n+260) = amt invested by J
:
then
{{{78/n}}} = N's interest rate in decimal form
J interest rate was 1% less, therefore
{{{78/n}}} - .01 = J's interest rate 
:
j's interest rate * j's amt = 78
({{{78/n}}}-.01)(n+260) = 78
FOIL
78 + {{{20280/n}}} - .01n - 2.6 = 78
subtract 78 from both sides
{{{20280/n}}} - .01n - 2.6 = 0
multiply by n, form  quadratic equation
20280 - .01n^2 - 2.6n = 0
Multiply by -100
n^2 + 260n - 2028000 = 0
you can use the quadratic formula but this will factor
(n+1560)(n-1300) = 0
the positive solution
n = $1300 is N's investment
Find the interest rate
{{{78/1300}}} = .06 or 6% int
:
:
Confirm this by finding J's amt and int
1300 + 260 = $1560
{{{78/1560}}} = .05 or 5%, on 1 percent less