Equations in Real Life | Math Coach Amy

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Key Ideas Easy Medium Hard

What to Remember

Name the parts

The constant is the starting amount. The coefficient is the rate. The other side is the total.

The variable counts how many times the rate is used.

Read an equation as a situation

You can write a situation from an equation by naming what the number next to the variable counts.

In 2n + 10 = 24, the 2 counts each extra item, 10 is the start, and 24 is the total.

Solve in the same order

Undo the starting amount first. Then undo the rate.

The solution tells how many times the rate was used.

Level 1

Easy

A cost starts with a fee, then adds the same amount each time.

Example

A phone plan costs 15 dollars plus 3 dollars for each gigabyte. The total is 36 dollars. How many gigabytes is that?

Let n be the number of gigabytes.

3n + 15 = 36

3n + 15 − 15 = 36 − 15

3n = 21

Divide both sides by 3.

n = 7

Answer: 7 gigabytes

A phone plan costs 20 dollars plus 5 dollars for each gigabyte. The total is 45 dollars. How many gigabytes is that?

Show Answer

Let n be the number of gigabytes.

5n + 20 = 45

5n + 20 − 20 = 45 − 20

5n = 25

Divide both sides by 5.

n = 5

Answer: 5 gigabytes

A taxi costs 3 dollars plus 2 dollars for each mile. The total is 17 dollars. How many miles is that?

Show Answer

Let n be the number of miles.

2n + 3 = 17

2n + 3 − 3 = 17 − 3

2n = 14

Divide both sides by 2.

n = 7

Answer: 7 miles

A game costs 10 points plus 8 points for each level. The total is 50 points. How many levels is that?

Show Answer

Let n be the number of levels.

8n + 10 = 50

8n + 10 − 10 = 50 − 10

8n = 40

Divide both sides by 8.

n = 5

Answer: 5 levels

A class costs 15 dollars plus 4 dollars for each student. The total is 47 dollars. How many students is that?

Show Answer

Let n be the number of students.

4n + 15 = 47

4n + 15 − 15 = 47 − 15

4n = 32

Divide both sides by 4.

n = 8

Answer: 8 students

A tank costs 12 dollars plus 6 dollars for each hour. The total is 48 dollars. How many hours is that?

Show Answer

Let n be the number of hours.

6n + 12 = 48

6n + 12 − 12 = 48 − 12

6n = 36

Divide both sides by 6.

n = 6

Answer: 6 hours

A phone plan costs 10 dollars plus 4 dollars for each gigabyte. The total is 34 dollars. How many gigabytes is that?

Show Answer

Let n be the number of gigabytes.

4n + 10 = 34

4n + 10 − 10 = 34 − 10

4n = 24

Divide both sides by 4.

n = 6

Answer: 6 gigabytes

A taxi costs 4 dollars plus 3 dollars for each mile. The total is 25 dollars. How many miles is that?

Show Answer

Let n be the number of miles.

3n + 4 = 25

3n + 4 − 4 = 25 − 4

3n = 21

Divide both sides by 3.

n = 7

Answer: 7 miles

A game costs 25 points plus 5 points for each level. The total is 60 points. How many levels is that?

Show Answer

Let n be the number of levels.

5n + 25 = 60

5n + 25 − 25 = 60 − 25

5n = 35

Divide both sides by 5.

n = 7

Answer: 7 levels

A class costs 8 dollars plus 6 dollars for each student. The total is 44 dollars. How many students is that?

Show Answer

Let n be the number of students.

6n + 8 = 44

6n + 8 − 8 = 44 − 8

6n = 36

Divide both sides by 6.

n = 6

Answer: 6 students

A tank costs 30 dollars plus 5 dollars for each hour. The total is 55 dollars. How many hours is that?

Show Answer

Let n be the number of hours.

5n + 30 = 55

5n + 30 − 30 = 55 − 30

5n = 25

Divide both sides by 5.

n = 5

Answer: 5 hours

Level 2

Medium

Something already has an amount, then adds the same amount each time.

Example

The savings jar already has 20 dollars and adds 5 dollars for each week. The goal is 55 dollars. How many weeks are needed?

Let n be the number of weeks.

5n + 20 = 55

5n + 20 − 20 = 55 − 20

5n = 35

Divide both sides by 5.

n = 7

Answer: 7 weeks

The savings jar already has 12 dollars and adds 4 dollars for each week. The goal is 40 dollars. How many weeks are needed?

Show Answer

Let n be the number of weeks.

4n + 12 = 40

4n + 12 − 12 = 40 − 12

4n = 28

Divide both sides by 4.

n = 7

Answer: 7 weeks

The game already has 40 points and adds 15 points for each level. The goal is 100 points. How many levels are needed?

Show Answer

Let n be the number of levels.

15n + 40 = 100

15n + 40 − 40 = 100 − 40

15n = 60

Divide both sides by 15.

n = 4

Answer: 4 levels

The class already has 12 points and adds 3 points for each student. The goal is 36 points. How many students are needed?

Show Answer

Let n be the number of students.

3n + 12 = 36

3n + 12 − 12 = 36 − 12

3n = 24

Divide both sides by 3.

n = 8

Answer: 8 students

The taxi already has 8 dollars and adds 3 dollars for each mile. The goal is 29 dollars. How many miles are needed?

Show Answer

Let n be the number of miles.

3n + 8 = 29

3n + 8 − 8 = 29 − 8

3n = 21

Divide both sides by 3.

n = 7

Answer: 7 miles

The phone plan already has 10 dollars and adds 5 dollars for each gigabyte. The goal is 40 dollars. How many gigabytes are needed?

Show Answer

Let n be the number of gigabytes.

5n + 10 = 40

5n + 10 − 10 = 40 − 10

5n = 30

Divide both sides by 5.

n = 6

Answer: 6 gigabytes

The tank already has 16 dollars and adds 4 dollars for each hour. The goal is 48 dollars. How many hours are needed?

Show Answer

Let n be the number of hours.

4n + 16 = 48

4n + 16 − 16 = 48 − 16

4n = 32

Divide both sides by 4.

n = 8

Answer: 8 hours

The savings jar already has 18 dollars and adds 6 dollars for each week. The goal is 48 dollars. How many weeks are needed?

Show Answer

Let n be the number of weeks.

6n + 18 = 48

6n + 18 − 18 = 48 − 18

6n = 30

Divide both sides by 6.

n = 5

Answer: 5 weeks

The game already has 30 points and adds 10 points for each level. The goal is 80 points. How many levels are needed?

Show Answer

Let n be the number of levels.

10n + 30 = 80

10n + 30 − 30 = 80 − 30

10n = 50

Divide both sides by 10.

n = 5

Answer: 5 levels

The class already has 14 points and adds 2 points for each student. The goal is 30 points. How many students are needed?

Show Answer

Let n be the number of students.

2n + 14 = 30

2n + 14 − 14 = 30 − 14

2n = 16

Divide both sides by 2.

n = 8

Answer: 8 students

The taxi already has 6 dollars and adds 4 dollars for each mile. The goal is 34 dollars. How many miles are needed?

Show Answer

Let n be the number of miles.

4n + 6 = 34

4n + 6 − 6 = 34 − 6

4n = 28

Divide both sides by 4.

n = 7

Answer: 7 miles

Level 3

Hard

Something starts with an amount and goes down by the same amount each time.

Example

The tank starts at 40 dollars and goes down by 5 dollars for each hour. It ends at 15 dollars. How many hours was that?

Let n be the number of hours.

−5n + 40 = 15

−5n + 40 − 40 = 15 − 40

−5n = −25

Divide both sides by −5.

n = 5

Answer: 5 hours

The tank starts at 50 miles and goes down by 6 miles for each hour. It ends at 20 miles. How many hours was that?

Show Answer

Let n be the number of hours.

−6n + 50 = 20

−6n + 50 − 50 = 20 − 50

−6n = −30

Divide both sides by −6.

n = 5

Answer: 5 hours

The phone plan starts at 80 dollars and goes down by 8 dollars for each gigabyte. It ends at 32 dollars. How many gigabytes was that?

Show Answer

Let n be the number of gigabytes.

−8n + 80 = 32

−8n + 80 − 80 = 32 − 80

−8n = −48

Divide both sides by −8.

n = 6

Answer: 6 gigabytes

The game starts at 100 points and goes down by 12 points for each level. It ends at 40 points. How many levels was that?

Show Answer

Let n be the number of levels.

−12n + 100 = 40

−12n + 100 − 100 = 40 − 100

−12n = −60

Divide both sides by −12.

n = 5

Answer: 5 levels

The savings jar starts at 60 dollars and goes down by 5 dollars for each week. It ends at 25 dollars. How many weeks was that?

Show Answer

Let n be the number of weeks.

−5n + 60 = 25

−5n + 60 − 60 = 25 − 60

−5n = −35

Divide both sides by −5.

n = 7

Answer: 7 weeks

The class starts at 90 points and goes down by 9 points for each student. It ends at 36 points. How many students was that?

Show Answer

Let n be the number of students.

−9n + 90 = 36

−9n + 90 − 90 = 36 − 90

−9n = −54

Divide both sides by −9.

n = 6

Answer: 6 students

The taxi starts at 70 dollars and goes down by 4 dollars for each mile. It ends at 42 dollars. How many miles was that?

Show Answer

Let n be the number of miles.

−4n + 70 = 42

−4n + 70 − 70 = 42 − 70

−4n = −28

Divide both sides by −4.

n = 7

Answer: 7 miles

The tank starts at 48 dollars and goes down by 6 dollars for each hour. It ends at 12 dollars. How many hours was that?

Show Answer

Let n be the number of hours.

−6n + 48 = 12

−6n + 48 − 48 = 12 − 48

−6n = −36

Divide both sides by −6.

n = 6

Answer: 6 hours

The phone plan starts at 64 dollars and goes down by 7 dollars for each gigabyte. It ends at 29 dollars. How many gigabytes was that?

Show Answer

Let n be the number of gigabytes.

−7n + 64 = 29

−7n + 64 − 64 = 29 − 64

−7n = −35

Divide both sides by −7.

n = 5

Answer: 5 gigabytes

The game starts at 120 points and goes down by 15 points for each level. It ends at 45 points. How many levels was that?

Show Answer

Let n be the number of levels.

−15n + 120 = 45

−15n + 120 − 120 = 45 − 120

−15n = −75

Divide both sides by −15.

n = 5

Answer: 5 levels

The savings jar starts at 45 dollars and goes down by 4 dollars for each week. It ends at 17 dollars. How many weeks was that?

Show Answer

Let n be the number of weeks.

−4n + 45 = 17

−4n + 45 − 45 = 17 − 45

−4n = −28

Divide both sides by −4.

n = 7

Answer: 7 weeks

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