Philip N. answered • 04/06/13

Certified 5-12 Math Teacher

Let A be the amount invested in Fund A, which earned 7%, and let B be the amount invested in Fund B, which earned 3%. We know that the sum of the amount earned from Fund A (7%×A) and the amount earned from Fund B (3%×B) is $138, or

(7%×A) + (3%×B) = (0.07×A) + (0.03×B) = $138 [1]

We also know that the sum of the amount invested in Fund A and the amount invested in Fund B is $2,600, or

A + B = $2600 [2]

We can solve equation [2] for B, giving us

B = $2,600-A [3]

Now we can substitute this value into equation [1], and solve for A.

(0.07×A) + [0.03×($2,600-A)] = $138 (substitution property of equality)

(0.07×A) + (0.03×$2,600) - (0.03×A) = $138 (distributive property of multiplication over subtraction)

(0.07×A) + $78 - 0.03×A = $138 (evaluate 0.03×$2,600)

(0.07×A) + $78 + -0.03×A = $138 (additive inverse property)

(0.07×A) + -0.03×A + $78 = $138 (commutative property of addition)

0.07×A + -0.03×A = $60 (subtraction property of equality)

(0.07 + -0.03)×A = $60 (distributive property of multiplication over addition)

(0.04)×A = $60 (evaluate 0.07 + -0.03)

A = $1,500 (division property of equality)

Substituting this value into equation [3], we have

B = $2,600 - A = $2,600 - $1,500 = $1,100

And finally, using equation [1] to check our result:

(0.07×A) + (0.03×B) = (0.07×$1,500) + (0.03×$1,100) = $105 + $33 = $138