Question

1. a 180 - second song is divided into 2 sections. the ratio of the two sections is 3:4. what is the length, to the nearest second, of the longer section?
2. the lengths of the 3 sides of a triangle are in the ratio 4:5:6. the perimeter of the triangle is 90 centimeters. what is the length, in centimeters, of the longest side of the triangle?
3. a new 75 - mile road is divided into 3 sections. the ratio of the 3 sections is 1:2:3. what is length, to the nearest half - mile, of the shortest section?
4. a recipe for 100 cookies requires 2.5 sticks of butter. about how many sticks of butter are required for 90 cookies?

Explanation:

Question 4

Step1: Find total parts of the ratio

The ratio of the two sections is \( 3:4 \), so the total number of parts is \( 3 + 4=7 \) parts.

Step2: Find the length per part

The total length of the song is 180 seconds. So the length of one part is \( \frac{180}{7}\approx25.71 \) seconds.

Step3: Find the length of the longer section

The longer section has a ratio of 4. So its length is \( 4\times\frac{180}{7}=\frac{720}{7}\approx103 \) seconds (to the nearest second).

Step1: Find total parts of the ratio

The ratio of the three sides is \( 4:5:6 \), so the total number of parts is \( 4 + 5+6 = 15 \) parts.

Step2: Find the length per part

The perimeter of the triangle is 90 centimeters. So the length of one part is \( \frac{90}{15} = 6 \) centimeters.

Step3: Find the length of the longest side

The longest side has a ratio of 6. So its length is \( 6\times6=36 \) centimeters.

Step1: Find total parts of the ratio

The ratio of the three sections is \( 1:2:3 \), so the total number of parts is \( 1+2 + 3=6 \) parts.

Step2: Find the length per part

The total length of the road is 75 miles. So the length of one part is \( \frac{75}{6}=12.5 \) miles.

Step3: Find the length of the shortest section

The shortest section has a ratio of 1. So its length is \( 1\times12.5 = 12.5 \) miles (which is already to the nearest half - mile).

Answer:

\( 103 \) seconds

Question 5