Abrother and a sister invested part of their $600 of allowance money at 4% and the remainder as 7%. their annual income from these two investments was equivalent to an income of 6% on the entire sum. how much was invested at each rate?

Define x and y :

Let the amount they invested in 4% be x
Let the amount they invested in 7% be y


Construct equations :

Total amount invested:
x + y = 600

The two investment is equivalent to 6% of the entire sum:
0.04x + 0.07y = 0.06 x 600
0.04x + 0.07y = 36


Solve for x and y :

x + y = 600    (1)
0.04x + 0.07y = 36 (2)

From equation (1):
x + y = 600
x = 600 - y Sub into (2)
0.04(600 - y) + 0.07y = 36
24 - 0.04y + 0.07y = 36
0.03y = 12
y = 400 Sub into (1)
x + 400 = 600
x = 200


Find amount invested :

4% investment = x = $200
7% investment = y = $400


They invested $200 in the 4% investment
                               and $400 in the 7% investment.