Q:

# A brother 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? Accepted Solution A: --------------------------------------------------- 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 ------------------------------------------------------------------------------------------------------ Answer: They invested$200 in the 4% investment
and \$400 in the 7% investment.
------------------------------------------------------------------------------------------------------