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# Systems of Equations and Reduced Row Echelon Form

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A company 403(b) plan allows employees to divide their investments among three mutual
funds: an aggressive growth fund, a hybrid fund, and an income fund. The aggressive growth
fund currently owns 90% stocks, 5% bonds, and 5% cash. The hybrid fund owns 60% stocks,
20% bonds, and 20% cash. The income fund owns 25% stocks, 50% bonds, and 25% cash.
Suppose an employee has \$10,000 to place in her 403(b) this year. For each of the following
investment proportions, tell whether it is possible for her to divide the \$10,000 among the
three funds so that the total amount invested in stocks, bonds, and cash are exactly in her
desired proportions. If such an investment is possible, tell how much money should be in-
vested in each of the three funds. Use a multisystem to do both parts simultaneously. You
may use your calculator to move the augmented matrix into rref form. You do not need to
show the row operations.
(a) 85% stocks, 10% bonds, and 5% cash
(b) 45% stocks, 35% bonds, and 20% cash