Problema Solution

"Use substitution strategy to solve a system of linear equations"

5000 was invested in two savings bonds for one year One bond earned interest at an annual rate of 2.5% The other bond earned 3.75% interest per year The total interest earned in one year was 162.50 How much money was invested in each bond? let x= let y=

Answer provided by our tutors

From the given question we can form two equations

i.e., x + y = 5000 ------------------------------1

       0.025x + 0.0375y = 162.50 -----------2

From equation 1

x + y = 5000

y = 5000 - x -----------------------------------3

By substituting equation 3 in 2:

0.025x + 0.0375(5000 - x) = 162.50

0.025x + 187.50 - 0.0375x = 162.50

187.50 - 162.50 = 0.0375x - 0.025x

25 = 0.0125x

So, x = 25/0.0125

       x = 2000

By substituting value of x in equation 1, we get

2000 + y = 5000

y = 5000 - 2000

y = 3000

So, 2000 was invested in a bond which yielded 2.5% interest per annum

And 3000 was invested in a bond which yielded 3.75% interest per annum.