A machine produces 440 bolts in 48 minutes. At the same rate, how many bolts would be produced in 30 minutes?

1 answer:

3 0

The units you want is $\frac{bolts}{min}$ , so you set up the following equation:
$\frac{440\ bolts}{48\ mins} = \frac{x}{30\ mins} \\
440*30=48*x\\
13200=48x\\
x=\frac{13200}{48}=275 \frac{bolts}{min}$

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2x + 12 = 1/3 (7/3x+4/3)

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Answer:

Step-by-step explanation:

2x + 12 = 1/3 (7/3x+4/3)

$2x+12=\frac{1}{3}*\frac{7x}{3}+\frac{1}{3}*\frac{4}{3}\\\\2x+12=\frac{7x}{9}+\frac{4}{9}\\\\2x-\frac{7x}{9}=\frac{4}{9}-12\\\\\frac{2x*9}{1*9}-\frac{7x}{9}=\frac{4}{9}-\frac{12*9}{1*9}\\\\\frac{18x}{9}-\frac{7x}{9}=\frac{4}{9}-\frac{108}{9}\\\\\frac{18x-7x}{9}=\frac{4-108}{9}\\\\\frac{11x}{9}=\frac{-104}{9}\\\\\\x=\frac{-104*9}{11*9}=\frac{-104}{11}=-9\frac{5}{11}$