Question

1. on a scale drawing, 1 inch represents 8 feet. if a garden is 24 feet long, how long is it on the scale drawing? 2) you have a recipe that serves 10 people and calls for 3 cups of flour. if you want to make the recipe for 20 people, how many cups of flour do you need? 3) which value of y makes this proportion true? $\frac{15}{35}=\frac{y}{84}$ 4) if the ratio of girls to boys in a class is 3:5, and there are 24 girls, how many boys are there? 5) order the following numbers from least to greatest: -8, 12, |8|, -$\frac{1}{4}$, -3.5 6) calculate the area of a rectangle with a length of 8 cm and a width of 5 cm. extended response 7) a scale drawing of the floor of a rectangular - shaped classroom is shown in the diagram below. the drawing has a scale of 1 inch to 14 feet. what is the area, in square feet, of the actual classroom? diagram of classroom floor

Explanation:

Step1: Set up proportion for scale - drawing problem

Let $x$ be the length on the scale - drawing. The proportion is $\frac{1}{8}=\frac{x}{24}$. Cross - multiply: $8x = 24$.

Step2: Solve for $x$

Divide both sides of the equation $8x = 24$ by 8: $x=\frac{24}{8}=3$ inches.

Step3: Set up proportion for recipe problem

Let $y$ be the number of cups of flour for 20 people. The proportion is $\frac{3}{10}=\frac{y}{20}$. Cross - multiply: $10y=3\times20 = 60$.

Step4: Solve for $y$

Divide both sides of the equation $10y = 60$ by 10: $y = 6$ cups.

Step5: Solve proportion for $y$ value

Given $\frac{15}{35}=\frac{y}{84}$, cross - multiply: $35y=15\times84$. First, calculate $15\times84 = 1260$. Then, $y=\frac{1260}{35}=36$.

Step6: Solve ratio problem

Let the number of boys be $z$. The ratio of girls to boys is $\frac{3}{5}=\frac{24}{z}$. Cross - multiply: $3z=24\times5 = 120$. Then, $z=\frac{120}{3}=40$ boys.

Step7: Order the numbers

First, $|8| = 8$. The numbers in order from least to greatest are: $-8,-3.5,-\frac{1}{4},|8|,12$.

Step8: Calculate rectangle area

The area formula for a rectangle is $A = l\times w$. Given $l = 8$ cm and $w = 5$ cm, then $A=8\times5 = 40$ $cm^{2}$.

Step9: Solve for actual classroom area

If 1 inch represents 14 feet, and the length on the scale - drawing is 2 inches and assume the width on the scale - drawing is 1 inch (not given in the problem statement, but if we consider a basic rectangle with one side given). The actual length $L=2\times14 = 28$ feet and the actual width $W = 1\times14=14$ feet. The area $A = L\times W=28\times14 = 392$ square feet.

Answer:

1. 3 inches
2. 6 cups
3. 36
4. 40 boys
5. $-8,-3.5,-\frac{1}{4},|8|,12$
6. 40 $cm^{2}$
7. 392 square feet