| Problem |
Solution |
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1) Barrett is an artist working on a tile collage. His canvas measures 8 m by 10 m. His tiles are squares of 40 cm side length. How many tiles will be needed to fill his collage? |
1. Convert the canvas measurements to cm = 800 x 1000
2. Compute the area of the canvas in sq. cm. = 800,000 sq. cm.
3. Divide this by the area of one tile =
8000/(40 x 40) = 800,000/1600 = 500
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2) There are two taxi services in your city. Cab-Xpress charges $5.25 for the first 5 miles and 22 cents per mile beyond that. Relaxi-Taxi charges $4.55 for the first 5 miles and 36 cents per mile beyond that. For what mileage is the cost of the two taxi services equal? |
Use M for the mileage of the trip.
1. The expression for the Cab-Xpress rate is
$5.25 + .22(M - 5)
2. The expression for the Relaxi-Taxi rate is
$4.55 + .36(M - 5)
3. Set these two expressions equal to each other and solve:
4.55 + .36(M - 5) = 5.25 + .22(M - 5)
.36(M - 5) - .22(M - 5) = 5.25 - 4.55
.14(M - 5) = .7
M - 5 = 5; M = 10
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3) A square painting is expanded by 4 ft on each of the four sides. Its new surface area after expansion is 196 sq. ft. What was the perimeter of the original painting? |
1. Take the square root of 196 to find the length of the side of the new square = 14 ft.
2. Subtract 4 from this side length = 10 ft.
3. Multiply by 4 = 40 ft.
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4) An equilateral triangle is enlarged so that the new triangle has an area that is nine times that of the initial triangle. What is the ratio of the new side length to the original side length? |
Call the initial side length 1 and the new side length s:
The area of an equilateral triangle is a2(√
3 ) / 4 = .433 a2
1. Ratio of the side lengths =
9 = .433 s2 = s2; s = 3
.433(1)
2. The ratio is 3/1
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5) A company makes five 32 inch televisions for every three 48 inch televisions it makes. If the company makes thirty-six 48 inch televisions, how many 32 inch televisions will it make? |
1. The ratio between 32 and 48 inch tv rates is 5/3
2. Multiply the number of 48-inch tvs by this ratio =
36 x (5/3) = 12 x 5 = 60
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