Math / Numbers & Operations

QuestionTyler has 24 quarters and 6 dimes. a. Write and explain the meaning of two ratios that could represent this situation. bil and.12:3 berause they ore able to be muitipled to get $24: 6$ b. Tyler puts all the coins in bags. Every bag has the same number of quarters and the same number of dimes. How many bags of coins can Tyler make? How many quarters and how many dimes are in each bag? c. Use ratio language to describe the relationship between the number of quarters and the numb of dimes in each bag from part (b).

Studdy Solution

STEP 1

1. Tyler has 24 quarters and 6 dimes.
2. Ratios can be used to compare the quantities of quarters and dimes.
3. The number of bags must evenly divide both the number of quarters and the number of dimes.
4. Each bag will have the same number of quarters and the same number of dimes.

STEP 2

1. Write and explain two ratios that represent the given quantities.
2. Determine the number of bags Tyler can make.
3. Describe the relationship between the number of quarters and the number of dimes in each bag.

STEP 3

Write the ratio of quarters to dimes.
$\text{Ratio of quarters to dimes} = \frac{24 \text{ quarters}}{6 \text{ dimes}} = \frac{24}{6} = 4:1$

STEP 4

Explain the meaning of the ratio 4:1.
The ratio 4:1 means that for every 4 quarters, there is 1 dime.

STEP 5

Write another ratio that represents the given quantities in reverse order.
$\text{Ratio of dimes to quarters} = \frac{6 \text{ dimes}}{24 \text{ quarters}} = \frac{6}{24} = 1:4$

STEP 6

Explain the meaning of the ratio 1:4.
The ratio 1:4 means that for every 1 dime, there are 4 quarters.

STEP 7

Determine the greatest common divisor (GCD) of 24 and 6.
$\text{GCD}(24, 6) = 6$

STEP 8

Divide the total number of quarters and dimes by the GCD to find the number of bags.
$\text{Number of bags} = \frac{24}{6} = 4$ $\text{Each bag will contain} = \frac{6}{6} = 1 \text{ dime}$

STEP 9

Calculate the number of quarters in each bag.
$\text{Number of quarters in each bag} = \frac{24}{4} = 6$

STEP 10

Summarize the number of bags and the contents of each bag.
Tyler can make 4 bags, each containing 6 quarters and 1 dime.

STEP 11

Use ratio language to describe the relationship between the number of quarters and the number of dimes in each bag.
The ratio of quarters to dimes in each bag is 6:1.
Solution: a. The two ratios that could represent the situation are: - 4:1 (quarters to dimes) - 1:4 (dimes to quarters) b. Tyler can make 4 bags. Each bag contains 6 quarters and 1 dime.
c. The ratio of quarters to dimes in each bag is 6:1.

Was this helpful?

Studdy Solution

STEP 1

1. Tyler has 24 quarters and 6 dimes.
2. Ratios can be used to compare the quantities of quarters and dimes.
3. The number of bags must evenly divide both the number of quarters and the number of dimes.
4. Each bag will have the same number of quarters and the same number of dimes.

STEP 2

1. Write and explain two ratios that represent the given quantities.
2. Determine the number of bags Tyler can make.
3. Describe the relationship between the number of quarters and the number of dimes in each bag.

STEP 3

Write the ratio of quarters to dimes.
$\text{Ratio of quarters to dimes} = \frac{24 \text{ quarters}}{6 \text{ dimes}} = \frac{24}{6} = 4:1$

STEP 4

Explain the meaning of the ratio 4:1.
The ratio 4:1 means that for every 4 quarters, there is 1 dime.

STEP 5

Write another ratio that represents the given quantities in reverse order.
$\text{Ratio of dimes to quarters} = \frac{6 \text{ dimes}}{24 \text{ quarters}} = \frac{6}{24} = 1:4$

STEP 6

Explain the meaning of the ratio 1:4.
The ratio 1:4 means that for every 1 dime, there are 4 quarters.

STEP 7

Determine the greatest common divisor (GCD) of 24 and 6.
$\text{GCD}(24, 6) = 6$

STEP 8

Divide the total number of quarters and dimes by the GCD to find the number of bags.
$\text{Number of bags} = \frac{24}{6} = 4$ $\text{Each bag will contain} = \frac{6}{6} = 1 \text{ dime}$

STEP 9

Calculate the number of quarters in each bag.
$\text{Number of quarters in each bag} = \frac{24}{4} = 6$

STEP 10

Summarize the number of bags and the contents of each bag.
Tyler can make 4 bags, each containing 6 quarters and 1 dime.

STEP 11

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

1. Tyler has 24 quarters and 6 dimes.2. Ratios can be used to compare the quantities of quarters and dimes.3. The number of bags must evenly divide both the number of quarters and the number of dimes.4. Each bag will have the same number of quarters and the same number of dimes.

STEP 2

1. Write and explain two ratios that represent the given quantities.2. Determine the number of bags Tyler can make.3. Describe the relationship between the number of quarters and the number of dimes in each bag.

STEP 3

Write the ratio of quarters to dimes.Ratio of quarters to dimes=24 quarters6 dimes=246=4:1 \text{Ratio of quarters to dimes} = \frac{24 \text{ quarters}}{6 \text{ dimes}} = \frac{24}{6} = 4:1 Ratio of quarters to dimes=6 dimes24 quarters​=624​=4:1

STEP 4

Explain the meaning of the ratio 4:1.The ratio 4:1 means that for every 4 quarters, there is 1 dime.

STEP 5

Write another ratio that represents the given quantities in reverse order.Ratio of dimes to quarters=6 dimes24 quarters=624=1:4 \text{Ratio of dimes to quarters} = \frac{6 \text{ dimes}}{24 \text{ quarters}} = \frac{6}{24} = 1:4 Ratio of dimes to quarters=24 quarters6 dimes​=246​=1:4

STEP 6

Explain the meaning of the ratio 1:4.The ratio 1:4 means that for every 1 dime, there are 4 quarters.

STEP 7

Determine the greatest common divisor (GCD) of 24 and 6.GCD(24,6)=6 \text{GCD}(24, 6) = 6 GCD(24,6)=6

STEP 8

Divide the total number of quarters and dimes by the GCD to find the number of bags.Number of bags=246=4 \text{Number of bags} = \frac{24}{6} = 4 Number of bags=624​=4 Each bag will contain=66=1 dime \text{Each bag will contain} = \frac{6}{6} = 1 \text{ dime} Each bag will contain=66​=1 dime

STEP 9

Calculate the number of quarters in each bag.Number of quarters in each bag=244=6 \text{Number of quarters in each bag} = \frac{24}{4} = 6 Number of quarters in each bag=424​=6

STEP 10

Summarize the number of bags and the contents of each bag.Tyler can make 4 bags, each containing 6 quarters and 1 dime.

STEP 11

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Tyler has 24 quarters and 6 dimes.
2. Ratios can be used to compare the quantities of quarters and dimes.
3. The number of bags must evenly divide both the number of quarters and the number of dimes.
4. Each bag will have the same number of quarters and the same number of dimes.

1. Write and explain two ratios that represent the given quantities.
2. Determine the number of bags Tyler can make.
3. Describe the relationship between the number of quarters and the number of dimes in each bag.

Write the ratio of quarters to dimes.
$\text{Ratio of quarters to dimes} = \frac{24 \text{ quarters}}{6 \text{ dimes}} = \frac{24}{6} = 4:1$

Explain the meaning of the ratio 4:1.
The ratio 4:1 means that for every 4 quarters, there is 1 dime.

Write another ratio that represents the given quantities in reverse order.
$\text{Ratio of dimes to quarters} = \frac{6 \text{ dimes}}{24 \text{ quarters}} = \frac{6}{24} = 1:4$

Explain the meaning of the ratio 1:4.
The ratio 1:4 means that for every 1 dime, there are 4 quarters.

Determine the greatest common divisor (GCD) of 24 and 6.
$\text{GCD}(24, 6) = 6$

Divide the total number of quarters and dimes by the GCD to find the number of bags.
$\text{Number of bags} = \frac{24}{6} = 4$ $\text{Each bag will contain} = \frac{6}{6} = 1 \text{ dime}$

Calculate the number of quarters in each bag.
$\text{Number of quarters in each bag} = \frac{24}{4} = 6$

Summarize the number of bags and the contents of each bag.
Tyler can make 4 bags, each containing 6 quarters and 1 dime.