Question: The length of a rectangle is four times its width. If the area is 100 m2. what is the length of the rectangle?
Answer: Let L be the length and W be the width of the rectangle. Hence L = 4 * W. We now use the area to write 80 = L * W. Substitute L by 4 W in the equation above 80 = 4 * W × W = 4 W^2. Solve for W and find L. 4 W^2 = 100. W^2 = 25, W = 5 and. L = 4 * 5 = 20 m. The answer is 20.
[Question]The perimeter of a triangle is 160 cm. If two of the sides are 40 cm and 50 cm, calculate the length of the third side?
[Answer]To get the perimeter, you add all the sides o the triangles, so the first two sides add up to 40 + 50 = 90 cm. If the perimeter of the triangle is 160, the remaining side is 160 - 90 = 70 cm. The answer is 70.
Q: On a school trip to the seashore, Alan and his friends collected shells. Alan collected four times as many shells as Ben did. Ben got a late start and only collected a third of what Laurie did. If Laurie collected 36 shells how many did Alan collect?
A: Ben collected 36 / 3 = 12 shells. Alan collected 12 * 4 = 48 shells. The answer is 48.
Question: Theodore can craft 10 stone statues and 20 wooden statues every month. A stone statue costs $20 and a wooden statue costs $5. He also pays 10 percent of his total earnings in taxes. How much is his total earning every month?
Answer: Theodore's total earnings from the stone statues are 10 x $20 = $200. His total earnings from wooden statues are 20 x $5 = $100. So his total earnings from the stone and wooden statue are $200 + $100 = $300. The amount he pays for the tax is $300 x 10 / 100 = $30. Therefore his total monthly earnings are $300 - $30 = $270. The answer is 270.
[Question]Fiona completed 36 math questions in an hour. Shirley was able to complete twice as many math questions within that same time, and Kiana completed half of the sum of Fiona and Shirley's math questions. If they each did the same number of questions the following hour, how many math questions did all three girls complete in 2 hours?
[Answer]Shirley completed 36 x 2 = 72 questions. The sum of Fiona and Shirley's questions is 36 + 72 = 108. Kiana completed 108 / 2 = 54 questions. In one hour, they completed 108 + 54 = 162 questions. In two hours, they completed 162 x 2 = 324 questions. The answer is 324.
[Question]The movie theater sells matinee tickets for $5, evening tickets for $12, and 3D tickets for $20. If they sell 200 matinee tickets, 300 evening tickets and 100 3D tickets, how much money do they make in total?
[Answer]
First find the total revenue from the matinee tickets: $5 / ticket * 200 tickets = $1000. Then find the total revenue from the evening tickets: $12 / ticket * 300 tickets = $3600. Then find the total revenue from the 3D tickets: $20 / ticket * 100 tickets = $2000. Then add the cost of each group of tickets to find the total cost: $1000 + $3600 + $2000 = $6600. The answer is 6600.