Question

vocabulary and concept check

1. writing describe two ways you can use a table to write a proportion.
2. writing what is your first step when solving \\(\frac{x}{15}=\frac{3}{5}\\)? explain.
3. open - ended write a proportion using an unknown value \\(x\\) and the ratio \\(5:6\\). then solve it.

practice and problem solving
write a proportion to find how many points a student needs to score on the test to get the given score.

1. test worth 50 points; test score of 40%
2. test worth 50 points; test score of 78%
3. test worth 80 points; test score of 80%
4. test worth 150 points; test score of 96%

use the table to write a proportion.
8.

	game 1	game 2
shots	14	\\(w\\)

9.

	may	june
entries	85	170

10.

	today	yesterday
hours	2.5	4

11.

	race 1	race 2
seconds	\\(x\\)	22.4

1. error analysis describe and correct the error in writing the proportion.

	monday	tuesday
ounces	8	16

\\(\frac{2.08}{16}=\frac{d}{8}\\) (with a red cross on the original wrong proportion)

1. t - shirts you can buy 3 t - shirts for $24. write a proportion that gives the cost \\(c\\) of buying 7 t - shirts.
2. computers a school requires 2 computers for every 5 students. write a proportion that gives the number \\(c\\) of computers needed for 145 students.
3. swim team the school team has 80 swimmers. the ratio of seventh - grade swimmers to all swimmers is \\(5:16\\). write a proportion that gives the number \\(s\\) of seventh - grade swimmers.

Explanation:

Let's solve problem 4 as an example:

Step1: Understand the problem

We need to find the number of points a student needs to score on a 50 - point test to get a 40% score. Let the number of points be $p$. The percentage score is calculated as $\frac{\text{Points scored}}{\text{Total points}}\times100\%$. So we can set up a proportion.

Step2: Set up the proportion

We know that $\frac{p}{50}=\frac{40}{100}$. This is because the ratio of the points scored to the total points should be equal to the ratio of the percentage score to 100 (since percentage is out of 100).

Step3: Solve for $p$

Cross - multiply: $100p = 50\times40$. Then $100p=2000$. Divide both sides by 100: $p = \frac{2000}{100}=20$.

Step1: Identify the ratio

In Game 1, the ratio of points to shots is $\frac{12}{14}$. In Game 2, the ratio of points to shots is $\frac{18}{w}$. Since the ratio of points to shots should be the same (assuming a constant shooting efficiency), we can set up a proportion.

Step2: Set up the proportion

$\frac{12}{14}=\frac{18}{w}$

Step3: Cross - multiply and solve

Cross - multiply: $12w=14\times18$. $14\times18 = 252$. Then $12w = 252$. Divide both sides by 12: $w=\frac{252}{12}=21$.

Step1: Identify the ratio

The cost per T - shirt should be constant. The ratio of the number of T - shirts to the cost for the first case is $\frac{3}{24}$, and for the second case (7 T - shirts and cost $c$) is $\frac{7}{c}$.

Step2: Set up the proportion

$\frac{3}{24}=\frac{7}{c}$

Step3: Cross - multiply and solve

Cross - multiply: $3c=24\times7$. $24\times7 = 168$. Then $3c = 168$. Divide both sides by 3: $c=\frac{168}{3}=56$.

Answer:

The student needs to score 20 points.

Let's solve problem 8: