5. diego has $100. he uses the ratio 3 : 2 to determine how much he can spend and how much he can save. consider using a diagram or table to help with your thinking.
a how much money will diego spend?
b how much money will diego save?
6. jada has a bag of 110 marbles. the ratio of red marbles to blue marbles is 4 : 1. consider using a diagram or table to help with your thinking.
a how many red marbles does jada have?
b how many blue marbles does jada have?
7. the first floor of a house contains a family room and a dining room. the combined area of these two rooms is 270 ft². the ratio of the area of the family room to the area of the dining room is 4 : 2. what is the area of each room? consider using this table to help with your thinking.
| family room (ft²) | dining room (ft²) | total area (ft²) |
| --- | --- | --- |
| | | |
| | | |
a what is the area of the family room?
b what is the area of the dining room?
8. a teacher is planning a field trip to the zoo. the zoo requires 3 chaperones for every 25 students. shawn says, \if there are 112 students in grade 6 going on this field trip, 12 chaperones are needed.\ is shawn correct? write yes or no. explain your thinking.

Question

5. diego has $100. he uses the ratio 3 : 2 to determine how much he can spend and how much he can save. consider using a diagram or table to help with your thinking.
  a how much money will diego spend?
  b how much money will diego save?
6. jada has a bag of 110 marbles. the ratio of red marbles to blue marbles is 4 : 1. consider using a diagram or table to help with your thinking.
  a how many red marbles does jada have?
  b how many blue marbles does jada have?
7. the first floor of a house contains a family room and a dining room. the combined area of these two rooms is 270 ft². the ratio of the area of the family room to the area of the dining room is 4 : 2. what is the area of each room? consider using this table to help with your thinking.
| family room (ft²) | dining room (ft²) | total area (ft²) |
| --- | --- | --- |
|  |  |  |
|  |  |  |
  a what is the area of the family room?
  b what is the area of the dining room?
8. a teacher is planning a field trip to the zoo. the zoo requires 3 chaperones for every 25 students. shawn says, \if there are 112 students in grade 6 going on this field trip, 12 chaperones are needed.\ is shawn correct? write yes or no. explain your thinking.

Accepted Answer

### Problem 5
#### Part a
# Explanation:
## Step1: Find total parts in ratio
The ratio of spend to save is $ 3:2 $, so total parts $ = 3 + 2 = 5 $.
## Step2: Find value of one part
Diego has $ \$100 $, so one part $ = \frac{100}{5} = 20 $.
## Step3: Calculate money spent
Money spent is $ 3 $ parts, so $ 3 \times 20 = 60 $.
# Answer:
$ \$60 $

#### Part b
# Explanation:
## Step1: Use total parts and one part value
From part a, total parts $ = 5 $, one part $ = 20 $.
## Step2: Calculate money saved
Money saved is $ 2 $ parts, so $ 2 \times 20 = 40 $.
# Answer:
$ \$40 $

### Problem 6
#### Part a
# Explanation:
## Step1: Find total parts in ratio
Ratio of red to blue marbles is $ 4:1 $, total parts $ = 4 + 1 = 5 $.
## Step2: Find value of one part
Total marbles $ = 110 $, so one part $ = \frac{110}{5} = 22 $.
## Step3: Calculate red marbles
Red marbles are $ 4 $ parts, so $ 4 \times 22 = 88 $.
# Answer:
$ 88 $ marbles

#### Part b
# Explanation:
## Step1: Use total parts and one part value
From part a, total parts $ = 5 $, one part $ = 22 $.
## Step2: Calculate blue marbles
Blue marbles are $ 1 $ part, so $ 1 \times 22 = 22 $.
# Answer:
$ 22 $ marbles

### Problem 7
#### Part a
# Explanation:
## Step1: Find total parts in ratio
Ratio of family room to dining room is $ 4:2 $, simplify to $ 2:1 $, total parts $ = 4 + 2 = 6 $ (or $ 2 + 1 = 3 $, but using original ratio).
## Step2: Find value of one part
Total area $ = 270 \, \text{ft}^2 $, one part $ = \frac{270}{6} = 45 $.
## Step3: Calculate family room area
Family room is $ 4 $ parts, so $ 4 \times 45 = 180 $.
# Answer:
$ 180 \, \text{ft}^2 $

#### Part b
# Explanation:
## Step1: Use total parts and one part value
From part a, total parts $ = 6 $, one part $ = 45 $.
## Step2: Calculate dining room area
Dining room is $ 2 $ parts, so $ 2 \times 45 = 90 $.
# Answer:
$ 90 \, \text{ft}^2 $

### Problem 8
# Explanation:
## Step1: Set up proportion
Let $ x $ be number of chaperones for $ 112 $ students. Proportion: $ \frac{3}{25} = \frac{x}{112} $.
## Step2: Solve for $ x $
Cross - multiply: $ 25x = 3\times112 = 336 $, so $ x=\frac{336}{25}=13.44 $.
Since chaperones must be whole number, we round up to $ 14 $ (or check how many groups of $ 25 $ in $ 112 $: $ 112\div25 = 4.48 $, so $ 5 $ groups? Wait, no, original ratio is $ 3 $ chaperones per $ 25 $ students. So for $ 100 $ students ($ 4\times25 $), chaperones $ = 4\times3 = 12 $, but $ 112 - 100 = 12 $ students left, which still need chaperones (since $ 12<25 $, but zoo requires $ 3 $ per $ 25 $, so we need another $ 3 $ chaperones? Wait, no, the proportion method: $ x=\frac{3\times112}{25}=13.44 $, so we need $ 14 $ chaperones (since we can't have $ 0.44 $ of a chaperone). Shawn says $ 12 $, which is incorrect.
# Answer:
No. Because using the proportion $ \frac{3}{25}=\frac{x}{112} $, we get $ x = \frac{3\times112}{25}=13.44 $, so we need at least $ 14 $ chaperones (since chaperones must be whole numbers), so Shawn is wrong.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 5

Part a

Step1: Find total parts in ratio

Step2: Find value of one part

Step3: Calculate money spent

Step1: Use total parts and one part value

Step2: Calculate money saved

Step1: Find total parts in ratio

Step2: Find value of one part

Step3: Calculate red marbles

Answer:

Part b