Question

set 52

1. kacey and starr found that if 3 times a number is decreased by 5 and this difference is doubled, the result is 14 less than twice the number. what is the number?
2. the average of the first 6 weights was 15 pounds. the average of the next 14 weights was 30 pounds. what was the overall average of all the weights?

Explanation:

Problem 1

Step1: Define variable for number

Let the number be $x$.

Step2: Translate to equation

$2(3x - 5) = 2x - 14$

Step3: Expand left side

$6x - 10 = 2x - 14$

Step4: Isolate $x$ terms

$6x - 2x = -14 + 10$
$4x = -4$

Step5: Solve for $x$

$x = \frac{-4}{4} = -1$

Step1: Calculate total first 6 weights

Total = $6 \times 15 = 90$ pounds

Step2: Calculate total next 14 weights

Total = $14 \times 30 = 420$ pounds

Step3: Find total weight & count

Total weight = $90 + 420 = 510$ pounds
Total count = $6 + 14 = 20$

Step4: Compute overall average

$\text{Average} = \frac{510}{20} = 25.5$

Answer:

$-1$

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Problem 2