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$Marco puts $200 into a savings account that earns 4.5% per year simple interest. a. What is the equation that represents this situation? y=200(1.045)^(**) b. How long will it take Marco to earn $50 in interest? {:[250=200(1.045)^(t)],[1.25=1.045^(t)]:} (C) Math By$

$4$ . Marco puts $\$ 200$ into a savings account that earns $4.5 \%$ per year simple interest. $\newline$ a. What is the equation that represents this situation? $\newline$ $y=200(1.045)^{*}$ $\newline$ b. How long will it take Marco to earn $\$ 50$ in interest? $\newline$ $\begin{array}{l} 250=200(1.045)^{t} \\ 1.25=1.045^{t} \end{array}$ $\newline$ (C) Math By

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Math Problems

Grade 6

Solve one-step multiplication and division equations: word problems

Full solution

4

. Marco puts

\$ 200

into a savings account that earns

4.5 \%

per year simple interest.

\newline

a. What is the equation that represents this situation?

\newline

y=200(1.045)^{*}

\newline

b. How long will it take Marco to earn

\$ 50

in interest?

\newline

\begin{array}{l} 250=200(1.045)^{t} \\ 1.25=1.045^{t} \end{array}

\newline

Write Equation: First, let's write down the equation for simple interest: $I = P \times r \times t$ , where $I$ is the interest, $P$ is the principal amount, $r$ is the rate of interest per year, and $t$ is the time in years.
Given Values: We know that Marco wants to earn $I = \$50$ in interest ( $I = \$50$ ), the principal amount ( $P$ ) is $\$200$ , and the rate of interest ( $r$ ) is $4.5\%$ per year, or $0.045$ in decimal form.
Plug into Formula: Now, plug these values into the simple interest formula to find the time $t$ : $\$50 = \$200 \times 0.045 \times t$ .
Isolate Time: To isolate $t$ , divide both sides of the equation by ( $\$200 * 0.045):$ t = \frac{\$50$}{(\$$200$ * $0$.$045$)}.
Calculate Time: Calculate the right side of the equation: $t = \frac{\$50}{\$9}$ .
Round to Nearest: $t = 5.555\ldots$ years, but since we can't have a fraction of a year in this context, we'll round to the nearest whole number, so $t = 6$ years.