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.