page 9

mr. austin recorded the number of books each student in his class read over winter break. he recorded the results below.

books read over winter break
frequency
0: x x x
1: x
2:
3: x x
4: x x x x x
5: x x x
6: x

x = 1 student

how many students did mr. austin survey from his class?

what is the area of jasons flag?

logan middle school is having a contest to design a new school flag. jason designs a flag in the shape of a trapezoid, as shown.
trapezoid with height 6 inches, parallel bases of 9 inches and 11 inches

there are 15 players on a volleyball team. the coach is ordering a sweatshirt for each player that costs $25 plus an additional $2 for each letter of the teams name on the back of the sweatshirt. she uses the expression 15(25+2x) to calculate the total cost for all of the sweatshirts. what is another way to write that expression?

alberts mom has 2,523 reward points from shopping at an online store. she uses the points to buy gift cards for free cups of coffee. each gift card costs 75 points.
- what is the greatest number of gift cards alberts mom can buy?
- how many reward points will she have left?

if 16 turkeys feed 72 people, then how many turkeys are needed to feed 126 people?
explain your thinking.

Question

page 9

mr. austin recorded the number of books each student in his class read over winter break. he recorded the results below.

books read over winter break
frequency
0: x x x
1: x
2:
3: x x
4: x x x x x
5: x x x
6: x

x = 1 student

how many students did mr. austin survey from his class?

what is the area of jasons flag?

logan middle school is having a contest to design a new school flag. jason designs a flag in the shape of a trapezoid, as shown.
trapezoid with height 6 inches, parallel bases of 9 inches and 11 inches

there are 15 players on a volleyball team. the coach is ordering a sweatshirt for each player that costs $25 plus an additional $2 for each letter of the teams name on the back of the sweatshirt. she uses the expression 15(25+2x) to calculate the total cost for all of the sweatshirts. what is another way to write that expression?

alberts mom has 2,523 reward points from shopping at an online store. she uses the points to buy gift cards for free cups of coffee. each gift card costs 75 points.
- what is the greatest number of gift cards alberts mom can buy?
- how many reward points will she have left?

if 16 turkeys feed 72 people, then how many turkeys are needed to feed 126 people?
explain your thinking.

Accepted Answer

{ "quality": "clear", "question_count": 5, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Mean Average", "Trapezoid Area", "Algebraic Simplification", "Dot Plot Interpretation" ], "new_concepts": [ "Proportional Reasoning" ], "current_concepts": [ "Mean Average", "Trapezoid Area", "Algebraic Simplification", "Dot Plot Interpretation", "Proportional Reasoning", "Division with Remainders" ] } ## Count the total number of students in Mr. Austin's class $$ \begin{aligned} \text{Students} &= 3\ (\text{at } 0) + 1\ (\text{at } 1) + 0\ (\text{at } 2) + 2\ (\text{at } 3) + 6\ (\text{at } 4) + 3\ (\text{at } 5) + 1\ (\text{at } 6) \ \text{Total} &= 3 + 1 + 0 + 2 + 6 + 3 + 1 = 16 \end{aligned} $$ ## Calculate the area of Jason's trapezoidal flag $$ \begin{aligned} b_1 &= 9\text{ in},\quad b_2 = 11\text{ in},\quad h = 6\text{ in} \ \text{Area} &= \frac{1}{2} \times (b_1 + b_2) \times h \ \text{Area} &= \frac{1}{2} \times (9 + 11) \times 6 = 10 \times 6 = 60\text{ sq inches} \end{aligned} $$ ## Simplify the algebraic expression for the sweatshirts $$ \begin{aligned} \text{Expression} &= 15(25 + 2x) \ \text{Simplified} &= 15 \times 25 + 15 \times 2x = 375 + 30x \end{aligned} $$ ## Solve the proportional reasoning problem for turkeys and people $$ \begin{aligned} \text{Ratio} &= \frac{72\text{ people}}{16\text{ turkeys}} = 4.5\text{ people per turkey} \ \text{Turkeys needed} &= \frac{126\text{ people}}{4.5\text{ people/turkey}} = 28\text{ turkeys} \end{aligned} $$ ## Calculate the gift cards and remaining reward points $$ \begin{aligned} \text{Total points} &= 2523,\quad \text{Cost per card} = 75 \ 2523 \div 75 &= 33\text{ R } 48 \ \text{Gift cards} &= 33 \ \text{Remaining points} &= 48 \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | How many students did Mr. Austin survey from his class? | 16 students | | 2 | What is the area of Jason's flag? | $60\text{ in}^2$ | | 3 | What is another way to write that expression? | $375 + 30x$ | | 4 | If 16 turkeys feed 72 people, then how many turkeys are needed to feed 126 people? | 28 turkeys | | 5 | What is the greatest number of gift cards Albert's mom can buy? How many reward points will she have left? | 33 gift cards; 48 points left | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Algebraic Simplification" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Count the total number of students in Mr. Austin's class

Calculate the area of Jason's trapezoidal flag

Simplify the algebraic expression for the sweatshirts

Solve the proportional reasoning problem for turkeys and people

Calculate the gift cards and remaining reward points

Answer:

No.	Problem	Answer
2	What is the area of Jason's flag?	\(60\text{ in}^2\)
3	What is another way to write that expression?	\(375 + 30x\)
4	If 16 turkeys feed 72 people, then how many turkeys are needed to feed 126 people?	28 turkeys
5	What is the greatest number of gift cards Albert's mom can buy? How many reward points will she have left?	33 gift cards; 48 points left