Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Mar 09, 2024

Phyllis invested $12,000 with a portion earning$ 4.5\% $interest and the rest earning$ 4\% $interest. After 1 year, the total interest earned was$ \ $525$ . Find the amount invested at each rate.

STEP 1

Question: Convert the simple interest rate of $4\frac{1}{2}\%$ to decimal form.
A) 0.045 B) 0.45 C) 4.5 D) 0.0045
Answer: A)

STEP 2

Question: If $x$ is the amount invested at the rate of $4\frac{1}{2}\%$ , which of the following represents the interest earned from this portion after 1 year?
A) $x \times 0.45$ B) $x \times 0.045$ C) $x \times 4.5$ D) $x \times 0.0045$
Answer: B)

STEP 3

Question: If the total amount invested is $12,000 and$ x is the amount invested at $4\frac{1}{2}\%$ , how much is invested at the rate of $4\%$ ?
A) $12,000 + x$ B) $12,000 - x$ C) $4\% \times x$ D) $4\% \times (12,000 - x)$
Answer: B)

STEP 4

Question: What is the correct equation to represent the total interest earned from both investments after 1 year?
A) $525 = x \times 0.045 + (12,000 + x) \times 0.04$ B) $525 = x \times 0.045 + 12,000 \times 0.04$ C) $525 = x \times 0.045 + (12,000 - x) \times 0.04$ D) $525 = x \times 0.04 + (12,000 - x) \times 0.045$
Answer: C)

STEP 5

Question: Solve the equation $45 = 0.005x$ for $x$ .
A) $x = 9,000$ B) $x = 900$ C) $x = 90$ D) $x = 9$
Answer: A)

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