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?","type":"single-choice","options":["A) $5 - 2n$","B) $2n - 5$","C) $2(n-5)$","D) $5n - 2$"],"correctAnswer":"B) $2n - 5$"}]},{"id":"group-15","questions":[{"id":15,"text":"Solve for $y$: $y + 9 = 15$","type":"single-choice","options":["A) $y=5$","B) $y=6$","C) $y=7$","D) $y=24$"],"correctAnswer":"B) $y=6$"}]},{"id":"group-16","questions":[{"id":16,"text":"A group of students is organizing a fundraiser. For every $3$ students who sell cookies, there are $2$ students who sell lemonade. If there are $18$ students selling cookies, how many students are selling lemonade? How many students are there in total participating in the fundraiser?","type":"short-answer","correctAnswer":"Let $C$ be the number of students selling cookies and $L$ be the number of students selling lemonade.\nThe ratio of cookie sellers to lemonade sellers is $3:2$. So, $\\frac{C}{L} = \\frac{3}{2}$.\nGiven $C = 18$, we have $\\frac{18}{L} = \\frac{3}{2}$.\nCross-multiply: $3L = 18 \\times 2$\n$3L = 36$\n$L = \\frac{36}{3}$\n$L = 12$ students selling lemonade.\nTotal students = Cookie sellers + Lemonade sellers = $18 + 12 = 30$ students.\nThere are $12$ students selling lemonade, and a total of $30$ students participating in the fundraiser."}]},{"id":"group-17","questions":[{"id":17,"text":"Sarah bought a new pair of shoes that cost $75. She also had to pay a $8\\%$ sales tax. What was the total amount Sarah paid for the shoes?","type":"short-answer","correctAnswer":"Cost of shoes = $75.\nSales tax rate = $8\\%$.\nSales tax amount = $8\\%$ of $75 = 0.08 \\times 75 = $6.00.\nTotal amount paid = Cost of shoes + Sales tax amount = $75 + $6.00 = $81.00.\nSarah paid a total of $81.00 for the shoes."}]},{"id":"group-18","questions":[{"id":18,"text":"The temperature at noon was $10^\\circ C$. By $6$ PM, it dropped by $12^\\circ C$. Then, overnight, it dropped another $5^\\circ C$. What was the temperature in the morning?","type":"short-answer","correctAnswer":"Initial temperature = $10^\\circ C$.\nDrop by $12^\\circ C$: $10 - 12 = -2^\\circ C$. (Temperature at 6 PM)\nDrop another $5^\\circ C$: $-2 - 5 = -7^\\circ C$. (Temperature in the morning)\nThe temperature in the morning was $-7^\\circ C$."}]},{"id":"group-19","questions":[{"id":19,"text":"Maria has some candies. She gives $7$ candies to her friend, and now she has $15$ candies left. Write and solve an equation to find out how many candies Maria had initially.","type":"short-answer","correctAnswer":"Let $c$ be the number of candies Maria had initially.\nShe gave away $7$ candies, so $c - 7$.\nShe has $15$ candies left, so $c - 7 = 15$.\nTo solve for $c$, add $7$ to both sides of the equation:\n$c - 7 + 7 = 15 + 7$\n$c = 22$.\nMaria initially had $22$ candies."}]},{"id":"group-20","questions":[{"id":20,"text":"A rectangle has a perimeter of $36$ cm. If the length of the rectangle is $10$ cm, what is its width? What is the area of the rectangle?","type":"short-answer","correctAnswer":"Perimeter of a rectangle $P = 2(l + w)$, where $l$ is length and $w$ is width.\nGiven $P = 36$ cm and $l = 10$ cm.\n$36 = 2(10 + w)$\nDivide both sides by $2$:\n$\\frac{36}{2} = 10 + w$\n$18 = 10 + w$\nSubtract $10$ from both sides:\n$18 - 10 = w$\n$w = 8$ cm.\nThe width of the rectangle is $8$ cm.\n\nArea of a rectangle $A = l \\times w$.\n$A = 10 \\text{ cm} \\times 8 \\text{ cm}$\n$A = 80 \\text{ cm}^2$.\nThe area of the rectangle is $80 \\text{ cm}^2$."}]}],"targetAudience":"6th Graders","creationTime":1789326070433,"lastVisited":1789326070433,"model":"predefined","timeTaken":0,"apiProvider":"static"}}}