Question

1. a fruit basket contains 8 apples, 6 oranges, and 10 bananas.

part a: what is the ratio of apples to the total number of fruits?
part b: does this represent a part to part relationship or a part to whole relationship; explain why.

1. in a bag of 80 marbles, 15 are red, 25 are blue, and the rest are green. what is the ratio of green marbles to the total number of marbles?
2. a school has 400 students, and 160 of them are in the sports program. what is the ratio of students in the sports program to those not in the program?
3. in a box of 48 chocolates, the ratio of milk chocolates to dark chocolates is 5:3. how many dark chocolates are in the box?
4. (compare two of given, (2) are equal and (2) are not

part a: write the letter of each to their proper ?
(choose ways)
part b: draw the response a part to part relationship or a part to whole relationship; explain why

1. (fill in the blank to make an equivalent ratio)

5 to 7 = ______ to 28

1. in the equivalent ratio \\(\frac{15}{4}=\frac{45}{y}\\), y equals ______
2. which ratio is not equivalent to 5:3?

a. 9:12 b. 12:15 c. 15:20 d. 18:24

1. a recipe calls for 3 cups of flour for every 2 cups of sugar. if you use 9 cups of flour, how many cups of sugar would you need?
2. in a school band, the ratio of trumpets to trombones is 5:3. if there are 20 trombones, how many trumpets are there?

a. 10
b. 20
c. 30
d. 40

Explanation:

Let's solve the problem about the box of chocolates (problem 5 on the left, maybe? Wait, the last problem on the left: "In a box of 48 chocolates, the ratio of milk chocolates to dark chocolates is 5:3. How many dark chocolates are in the box?"). Let's solve that.

Step1: Find total parts of the ratio

The ratio of milk to dark is \( 5:3 \), so total parts \( = 5 + 3 = 8 \).

Step2: Find value of one part

Total chocolates are 48, so one part \( = \frac{48}{8} = 6 \).

Step3: Calculate dark chocolates

Dark chocolates are 3 parts, so \( 3 \times 6 = 18 \)? Wait, no, wait: ratio milk:dark is 5:3, so dark is 3 parts. Wait, 5+3=8 parts. 48 divided by 8 is 6. So dark chocolates: 36=18? Wait, maybe I misread. Wait, the problem says "milk chocolates to dark chocolates is 5:3". So milk is 5 parts, dark is 3 parts. Total parts 8. 48/8=6. So dark is 36=18. Wait, but maybe the problem is different. Wait, let's check again.

Wait, maybe the problem is the one with school band: "In a school band, the ratio of trumpets to trombones is 5:3. If there are 20 trombones, how many trumpets are there?" Wait, no, the options are 10,20,30,40. Wait, maybe I mixed up. Let's take the chocolate problem first.

Wait, the chocolate problem: box of 48 chocolates, ratio milk to dark is 5:3. How many dark?

Total parts: 5 + 3 = 8.

Each part: 48 / 8 = 6.

Dark chocolates: 3 * 6 = 18.

But maybe the school band problem: ratio trumpets to trombones is 5:3. If trombones are 20? Wait, no, the options are 10,20,30,40. Wait, maybe the trombones are 12? No, the problem says "If there are 20 trombones" – wait, no, maybe the trombones are 12? Wait, no, the options are A.10, B.20, C.30, D.40. Let's solve that.

Ratio trumpets (T) to trombones (Tr) is 5:3. So T/Tr = 5/3.

If Tr = 20? No, that would give T = (5/3)*20 ≈ 33.33, not in options. Wait, maybe Tr is 12? No, the problem says "If there are 20 trombones" – wait, maybe a typo. Wait, maybe the trombones are 12? No, the options are 10,20,30,40. Wait, maybe the ratio is 5:3, and trombones are 12? No, let's check the chocolate problem again.

Wait, the chocolate problem: 48 chocolates, ratio 5:3. So milk is 5x, dark is 3x. 5x + 3x = 48 → 8x=48 → x=6. So dark is 3*6=18. So answer is 18.

But let's take the recipe problem: "A recipe calls for 3 cups of flour for every 2 cups of sugar. If you use 9 cups of flour, how many cups of sugar would you need?"

Step1: Set up proportion

Flour : Sugar = 3 : 2. Let sugar be \( x \). So \( \frac{3}{2} = \frac{9}{x} \).

Step2: Cross-multiply

\( 3x = 2 \times 9 \) → \( 3x = 18 \) → \( x = 6 \).

So sugar needed is 6 cups.

But let's choose one problem. Let's take the recipe problem.

Step1: Define the ratio

Flour to sugar ratio is \( 3:2 \), meaning \( \frac{\text{Flour}}{\text{Sugar}} = \frac{3}{2} \).

Step2: Set up proportion for 9 cups flour

Let \( x \) be sugar cups. Then \( \frac{3}{2} = \frac{9}{x} \).

Step3: Solve for \( x \)

Cross-multiply: \( 3x = 2 \times 9 \) → \( 3x = 18 \) → \( x = \frac{18}{3} = 6 \).

Answer:

6