Evaluate $r s+14 s$ when $r=6$ and $s=\frac{1}{4}$.
Answer (2)
Substitute r = 6 and s = 4 1 into the expression rs + 14 s .
Calculate 6 × 4 1 = 2 3 .
Calculate 14 × 4 1 = 2 7 .
Add the results: 2 3 + 2 7 = 5 . The final answer is 5 .
Explanation
Understanding the Problem We are asked to evaluate the expression rs + 14 s given that r = 6 and s = 4 1 . This means we need to substitute these values into the expression and simplify.
Substitution First, substitute the given values into the expression: rs + 14 s = ( 6 ) ( 4 1 ) + 14 ( 4 1 ) .
Multiplication Next, we perform the multiplications: 6 × 4 1 = 4 6 = 2 3 and 14 × 4 1 = 4 14 = 2 7 .
Addition Now, we add the two results: 2 3 + 2 7 = 2 3 + 7 = 2 10 = 5 .
Final Answer Therefore, the value of the expression rs + 14 s when r = 6 and s = 4 1 is 5 .
Examples
Imagine you're calculating the total cost of ingredients for a recipe. 'r' could represent the number of batches you're making, and 's' could be the cost of a key ingredient per batch. The expression rs + 14 s then calculates the total cost, where 'rs' is the cost of the key ingredient for 'r' batches, and '14s' is the cost of another ingredient that's needed in a fixed amount (14 units) per batch. Evaluating this expression helps you determine the overall expense for your recipe, ensuring you stay within budget.
The value of the expression rs + 14 s when substituting r = 6 and s = 4 1 evaluates to 5 . This is calculated by finding the product of rs and 14 s separately before adding the results together. Therefore, the final answer is 5 .
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