A gallon of stain is enough to cover 200 square feet of decking. Bradley has two areas of decking he would like to cover with stain. One rectangular area is 23 feet by 10.4 feet, and the other is 10.5 feet by 7.2 feet. Which expression gives the number of gallons of stain Bradley will need?
[(23)(10.5)+(10.4)(7.2)]+200
[(23)(10.4)+(10.5)(7.2)]+200
[(23)(10.5)+(10.4)(7.2)] / 200
[(23)(10.4)+(10.5)(7.2)] / 200
Answer (2)
Calculate the area of the first rectangular decking: A re a 1 = 23 × 10.4 = 239.2 square feet.
Calculate the area of the second rectangular decking: A re a 2 = 10.5 × 7.2 = 75.6 square feet.
Calculate the total area: T o t a l A re a = A re a 1 + A re a 2 = 239.2 + 75.6 = 314.8 square feet.
Calculate the number of gallons needed: G a ll o n s = 200 T o t a l A re a = 200 314.8 = 1.574 . Therefore, the expression is 200 ( 23 × 10.4 ) + ( 10.5 × 7.2 ) .
Explanation
Problem Analysis Let's break down this problem. We need to find the total area of the decking Bradley wants to stain and then determine how many gallons of stain he needs to cover that area. Each gallon covers 200 square feet.
Calculate Area 1 First, we calculate the area of the first rectangular section, which is 23 feet by 10.4 feet. The area is calculated as follows: A re a 1 = l e n g t h × w i d t h = 23 × 10.4 = 239.2 square feet
Calculate Area 2 Next, we calculate the area of the second rectangular section, which is 10.5 feet by 7.2 feet. The area is calculated as follows: A re a 2 = l e n g t h × w i d t h = 10.5 × 7.2 = 75.6 square feet
Calculate Total Area Now, we add the two areas together to find the total area: T o t a l A re a = A re a 1 + A re a 2 = 239.2 + 75.6 = 314.8 square feet
Calculate Gallons Needed Finally, we determine the number of gallons needed by dividing the total area by the coverage of one gallon (200 square feet): G a ll o n s N ee d e d = C o v er a g e P er G a ll o n T o t a l A re a = 200 314.8 = 1.574 gallons Since Bradley can only buy whole gallons, he will need to buy 2 gallons of stain.
Final Expression The expression that gives the number of gallons of stain Bradley will need is: 200 ( 23 × 10.4 ) + ( 10.5 × 7.2 ) This corresponds to the option that calculates the total area and then divides by 200 to find the number of gallons.
Examples
When planning a garden, calculating areas is essential for determining how much soil, fertilizer, or mulch is needed. For instance, if you have a rectangular garden bed that is 12 feet long and 8 feet wide, the area is 12 × 8 = 96 square feet. Knowing this, you can accurately purchase the required amount of materials to ensure your plants thrive. This same principle applies to various home improvement projects, such as painting walls or laying tiles, where accurate area calculations prevent material shortages or waste.
To find out how many gallons of stain Bradley needs, we calculate the total area of the two decking sections, which is 314.8 square feet. The number of gallons required is found by dividing this total area by the coverage of one gallon (200 square feet), resulting in 1.574 gallons, which rounds up to 2 gallons. The appropriate expression for this calculation is 200 ( 23 × 10.4 ) + ( 10.5 × 7.2 ) .
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