MATH SOLVE

8 months ago

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:

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Define x and y :

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Let the amount they invested in 4% be x

Let the amount they invested in 7% be y

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Construct equations :

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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

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Solve for x and y :

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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

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Find amount invested :

---------------------------------------------------

4% investment = x = $200

7% investment = y = $400

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Answer: They invested $200 in the 4% investment

and $400 in the 7% investment.

------------------------------------------------------------------------------------------------------

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.

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