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Difficulty: MediumFractions, Decimals, and Percentages

A community theater group allocated a total budget of $1,500\$1,500 to create costumes for an upcoming production. Exactly 14\frac{1}{4} of the budget was spent on fabric, 0.300.30 of the budget was spent on specialized footwear, and 15\frac{1}{5} of the budget was spent on sewing accessories. The remaining amount of the budget was spent on theatrical wigs. What amount, in dollars, did the theater group spend on theatrical wigs?

  1. A
    $300\$300
  2. $375\$375Answer
  3. C
    $450\$450
  4. D
    $975\$975
  5. E
    $1,125\$1,125

Answer

The theater group spent $375\$375 on theatrical wigs.
The correct answer of $375\$375 is found by determining each individual expense and subtracting their sum from the total budget. Fabric accounts for 14\frac{1}{4} of $1,500\$1,500, which is $375\$375. Footwear accounts for 0.300.30 of $1,500\$1,500, which is $450\$450. Sewing accessories account for 15\frac{1}{5} of $1,500\$1,500, which is $300\$300. Combined, these three categories equal $375+$450+$300=$1,125\$375 + \$450 + \$300 = \$1,125. Subtracting $1,125\$1,125 from the total budget of $1,500\$1,500 leaves $375\$375 for theatrical wigs.

Step-by-Step Solution

1
Calculate the dollar amount spent on fabric
14×$1,500=$375\frac{1}{4} \times \$1,500 = \$375
Multiply the fraction representing fabric by the total budget.
2
Calculate the dollar amount spent on footwear
0.30×$1,500=$4500.30 \times \$1,500 = \$450
Multiply the decimal representing footwear by the total budget.
3
Calculate the dollar amount spent on sewing accessories
15×$1,500=$300\frac{1}{5} \times \$1,500 = \$300
Multiply the fraction representing accessories by the total budget.
4
Sum the three known category expenses
\$375 + \$450 + \$300 = \$1,125
Add the expenses together to determine the total spent before wigs.
5
Subtract the sum of known expenses from the total budget
\$1,500 - \$1,125 = \$375
The remaining portion of the budget is allocated to theatrical wigs.

Key Concept

Converting fractions and decimals to quantities of a total amount and calculating remaining portions.
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Topics

Fractions, Decimals, and Percentages

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