Suppose you're given the formula $R=s+2t$. If you know that $s$ is three times greater than $t$, how could you rewrite the formula?
A. $R=3(s+2t)$
B. $R=5s$
C. $R=5t$
D. $R=3(s+t)$
Answer (2)
Given R = s + 2 t and s = 3 t .
Substitute s = 3 t into the formula: R = 3 t + 2 t .
Simplify the expression: R = 5 t .
The rewritten formula is R = 5 t .
Explanation
Understanding the Problem We are given the formula R = s + 2 t and the information that s is three times greater than t , which means s = 3 t . We want to rewrite the formula R = s + 2 t using this relationship.
Substitution Since s = 3 t , we can substitute 3 t for s in the formula R = s + 2 t . This gives us R = 3 t + 2 t .
Simplifying the Expression Now, we simplify the expression by combining like terms: R = 3 t + 2 t = 5 t . So, R = 5 t .
Expressing t in terms of s Alternatively, we can express t in terms of s . Since s = 3 t , we can divide both sides by 3 to get t = 3 s . Substituting this into the formula R = s + 2 t , we get R = s + 2 ( 3 s ) .
Simplifying the Expression (Alternative) Simplifying this expression, we have R = s + 3 2 s . To combine these terms, we need a common denominator, which is 3. So, R = 3 3 s + 3 2 s = 3 5 s . This can also be written as R = 3 5 s . However, this option is not given in the choices.
Final Answer Comparing our result R = 5 t with the given options, we see that option C, R = 5 t , matches our result. Therefore, the correct answer is C.
Examples
Understanding how to rewrite formulas by substitution is useful in many real-life situations. For example, if you are calculating the total cost of a project where labor costs are dependent on the number of hours worked, and material costs are fixed, you can rewrite the total cost formula to depend only on the number of hours if you know the relationship between labor cost and hours. This simplifies your calculations and makes it easier to estimate project costs.
We rewrote the formula R = s + 2 t using the relationship s = 3 t to get R = 5 t . The correct answer is option C, which states R = 5 t .
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