Question

exercises
there are 3 red, 7 blue, and 5 yellow balloons.

1. write the ratio of blue balloons to total balloons in all three forms. write your answer in simplest form.
2. tell whether the ratio of red to blue balloons or the ratio of yellow balloons to total balloons is greater.

exercises
find each average rate of speed.

1. 540 ft in 90 s 7. 436 mi in 4 hr

find each unit price. then decide which is the better buy.

1. \\(\frac{\\$56}{25\text{ gal}}\\) or \\(\frac{\\$32.05}{15\text{ gal}}\\) 9. \\(\frac{\\$160}{5\text{ g}}\\) or \\(\frac{\\$315}{9\text{ g}}\\)

Explanation:

Question 4

Step1: Calculate total balloons

Total balloons = 3 (red) + 7 (blue) + 5 (yellow) = 15.

Step2: Find the ratio of blue to total

Blue balloons = 7, total = 15. So the ratio is 7:15 (colon form), $\frac{7}{15}$ (fraction form), and 7 to 15 (word form). Since 7 and 15 have no common factors other than 1, it's in simplest form.

Step1: Calculate ratio of red to blue

Red = 3, blue = 7. Ratio is \( \frac{3}{7} \approx 0.4286 \).

Step2: Calculate ratio of yellow to total

Yellow = 5, total = 15. Ratio is \( \frac{5}{15} = \frac{1}{3} \approx 0.3333 \).

Step3: Compare the two ratios

Since \( 0.4286 > 0.3333 \), the ratio of red to blue is greater.

Step1: Recall speed formula

Speed = distance / time.

Step2: Substitute values

Distance = 540 ft, time = 90 s. So speed = \( \frac{540}{90} = 6 \) ft/s.

Answer:

Colon form: \( 7:15 \), Fraction form: \( \frac{7}{15} \), Word form: \( 7 \) to \( 15 \)

Question 5