Question

1. consider the ratios 3:5 and 21:d. what must c and d be for the ratios to be equivalent? 4. the tape - diagram represents the ratio of the number of free throws made to the number of free throws missed at a basketball game. number of free throws made rectangles number of free throws missed rectangles a. if this pattern continues and 12 free throws are made, what is the total number of free attempts in the game? b. if this pattern continues and there are a total of 33 free throw attempts in the game, how many free throws are made? how many free throws are missed? 5. a sidewalk chalk recipe calls for 1 ounce of cornstarch for every 3 ounces of baking soda. a. draw a tape diagram that represents the ratio of the number of ounces of cornstarch to the number of ounces of baking soda.

Explanation:

3.

Step1: Set up proportion

For equivalent ratios $\frac{3}{5}=\frac{21}{D}$, we can cross - multiply.
$3D = 21\times5$

Step2: Solve for $D$

$D=\frac{21\times5}{3}=35$. There is no $c$ in the problem statement for this ratio problem, likely a mis - type. If we assume $c$ is not relevant, the value of $D$ for the ratios to be equivalent is 35.

4a.

Step1: Determine ratio from tape - diagram

The tape - diagram shows a ratio of free throws made to free throws missed of 6:5. Let the number of free throws made be $6x$ and the number of free throws missed be $5x$. Given $6x = 12$, then $x = 2$.

Step2: Calculate total free - throw attempts

The total number of free - throw attempts is $6x+5x=11x$. Substituting $x = 2$, we get $11\times2 = 22$.

4b.

Step1: Determine ratio sum

The ratio of free throws made to free throws missed is 6:5, so the sum of the ratio parts is $6 + 5=11$.

Step2: Find the multiplier

If the total number of free - throw attempts is 33, and the sum of the ratio parts is 11, then the multiplier $x=\frac{33}{11}=3$.

Step3: Calculate number of made and missed free throws

The number of free throws made is $6x = 6\times3=18$. The number of free throws missed is $5x = 5\times3 = 15$.

Answer:

1. $D = 35$

4a. 22
4b. Made: 18, Missed: 15