Jackson is painting the side of his school. He paints a wall that has an area of 41 1/3 square yards. He uses 2 1/3 gallons of orang paint. What is Jackson's rate of paint coverage in square yards per gallon?
The label on the paint container says that the average coverage rate is 275 square feet per gallon. what is the difference in square feet per gallon between Jackson's rate of paint coverage and the average rate indicated on the container? (Note: 1 square yard = 9 square feet)
41 1/3 / 2 1/3
= 124 / 7 = 17.7 yards^2 / gal
17.7 * 9 = 159 ft^2/gal
275 - 159 = 116 difference
41 1/3 sq yds divided by 2 1/3 gallons
You need to use improper fractions
124/3 divided by 7/3
124/3 times 3/7
124/7 sq yds per gallon
which you can change to a mixed number.
To find out what Jack is getting you need to multiply the answer above by 9 since 1 sq yard = 9 square feet.
Compare that answer with the given on the can.
To find Jackson's rate of paint coverage in square yards per gallon, we need to divide the area he painted by the amount of paint he used.
1. Convert the area of 41 1/3 square yards to a mixed number:
41 1/3 = 41 + 1/3 = 41 + (1/3 * 9/9) = 41 + 9/27 = 41 + 1/3 = 124/3 square yards
2. Convert the amount of paint used, 2 1/3 gallons, to a mixed number:
2 1/3 = 2 + 1/3 = 2 + (1/3 * 3/3) = 2 + 3/9 = 2 + 1/3 = 7/3 gallons
3. Calculate the rate of paint coverage in square yards per gallon:
Rate = Area / Paint used
Rate = (124/3) square yards / (7/3) gallons
Rate = (124/3) * (3/7) square yards per gallon
Rate = 124/7 square yards per gallon
So, Jackson's rate of paint coverage is 124/7 square yards per gallon.
To find the difference in square feet per gallon between Jackson's rate of paint coverage and the average rate indicated on the container, we need to convert both rates to square feet and then subtract.
1. Convert Jackson's rate from square yards per gallon to square feet per gallon:
Jackson's rate = (124/7 square yards per gallon) * (9 square feet / 1 square yard)
Jackson's rate = (124/7) * (9) square feet per gallon
Jackson's rate = 1116/7 square feet per gallon
2. Convert the average rate of 275 square feet per gallon to square yards per gallon:
Average rate = 275 square feet / 9 square feet per square yard
Average rate = 275/9 square yards per gallon
3. Calculate the difference in square feet per gallon:
Difference = Jackson's rate - Average rate
Difference = (1116/7 square feet per gallon) - (275/9 square yards per gallon)
To subtract these fractions, we need to find a common denominator:
The least common multiple of 7 and 9 is 63.
Difference = ((1116/7) * (9/9) - (275/9) * (7/7)) square yards per gallon
Difference = (10044/63 - 1925/63) square yards per gallon
Difference = 8120/63 square yards per gallon
Therefore, the difference in square feet per gallon between Jackson's rate of paint coverage and the average rate indicated on the container is 8120/63 square yards per gallon.