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Literal Equations

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Practice solving and using literal equations.

Tahmar knows the formula for simple interest is [tex] I = Prt [/tex], where [tex] I [/tex] represents the simple interest on an amount of money, [tex] P [/tex], for [tex] t [/tex] years at a rate [tex] r [/tex]. She transforms the equation to isolate [tex] P [/tex]:

[tex]\[ P = \frac{I}{rt} \][/tex]

Using this formula, what is the amount of money, [tex] P [/tex], that will generate \$20 at a 5% interest rate over 5 years?

[tex]\[ \boxed{ } \][/tex]



Answer :

GinnyAnswer
Sure, let's solve this step-by-step:

1. Given Information:
- Simple Interest ([tex]$I$[/tex]) = [tex]$20 - Interest Rate ($[/tex]r[tex]$) = 5% = 0.05 - Time ($[/tex]t[tex]$) = 5 years - We need to find the principal amount ($[/tex]P[tex]$). 2. Formula for Simple Interest: The formula for simple interest is given by: \[ I = Prt \] where: - $[/tex]I[tex]$ is the simple interest. - $[/tex]P[tex]$ is the principal amount. - $[/tex]r[tex]$ is the interest rate. - $[/tex]t[tex]$ is the time in years. 3. Isolate $[/tex]P[tex]$: We need to solve the equation for the principal amount $[/tex]P[tex]$. So, we rearrange the formula: \[ P = \frac{I}{rt} \] 4. Substitute the Given Values: - $[/tex]I = 20[tex]$ - $[/tex]r = 0.05[tex]$ - $[/tex]t = 5[tex]$ Plug these values into the formula: \[ P = \frac{20}{0.05 \times 5} \] 5. Calculate the Principal Amount: First, compute the denominator: \[ 0.05 \times 5 = 0.25 \] Then, divide the interest by this product: \[ P = \frac{20}{0.25} = 80 \] So, the principal amount $[/tex]P[tex]$ that will generate $[/tex]20 at a 5% interest rate over 5 years is $80.

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