A municipal water authority pumps water into a storage reservoir. During a drought conserv… — ACT

A municipal water authority pumps water into a storage reservoir. During a drought conservation phase, the authority reduces its standard daily pumping volume by $35\%$ . If the resulting reduced daily pumping volume is $W$ acre-feet, which of the following equations correctly expresses the standard daily pumping volume, $S$ , in acre-feet, in terms of $W$ ?

$S = \frac{W}{0.65}$ Answer
B
$S = 0.65W$
C
$S = \frac{W}{0.35}$
D
$S = 0.35W$
E
$S = W + 0.35$

Answer

The standard daily pumping volume is given by

S = \frac{W}{0.65}

Reducing the standard volume

S

35\%

leaves

65\%

S

, which can be written algebraically as

0.65S

. Since this reduced amount equals

W

, the relationship is

0.65S = W

. Dividing both sides by

0.65

isolates

S

to give the one-step equation solution

S = \frac{W}{0.65}

Step-by-Step Solution

Express the reduced volume in terms of the standard volume

S

Reduced volume

= S - 0.35S = 0.65S

35\%

reduction leaves

100\% - 35\% = 65\%

of the original standard volume

S

Set up the one-step algebraic equation matching the given variable

W

0.65S = W

The reduced volume is defined as

W

acre-feet.

Solve the one-step equation for

S

S = \frac{W}{0.65}

Divide both sides of the equation by

0.65

to isolate

S

Key Concept

Formulating and solving a one-step algebraic equation involving a percentage decrease.

Alternative Method

Convert

65\%

to the fraction

\frac{13}{20}

. Then

\frac{13}{20}S = W

, which yields

S = \frac{20}{13}W = \frac{W}{0.65}

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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