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1) Members at a yoga school pay $10 per class plus a one-time $100 membership fee. Non-members pay$15 per class. How many classes would a member have to take to save money compared to taking classes as a non-member?

2) Translate the statement into an equation. Then solve the equation. The sum of 8 and 3 times a number is 23.

6) Members at a yoga school pay $7 per class plus a one-time $120 membership fee. Non-members pay $11 per class. How many classes would a member have to take to save money compared to taking classes as a non-member?

Answer all questions please, and if u can show u work, please...

3)A rental car costs $36 for one day plus an additional $0.42 per mile. What is the cost of renting a car for one day and driving it 78 miles?

4) Alice earns 1.5 times her normal hourly rate for each hour she works after 40 hours in a week. She worked 50 hours this week and earned $660. What is her normal hourly rate?

5) Cynthia orders 27 prints of a photograph she took. It costs her a total of $242.73. Which equation can be used to find how much each print cost?

Respuesta :

calculista

Answer:

Part 1) The number of classes must be greater than 20

Part 2) see the explanation

Part 3) [tex]\$68.76[/tex]

Part 4) [tex]\$12\ per\ hour[/tex]

Part 5) The equation that can be used is [tex]27x=242.73[/tex]  and the cost of one print is [tex]\$8.99[/tex]

Part 6) The number of classes must be greater than 30

Step-by-step explanation:

Part 1) we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

Members

The slope is [tex]m=\$10\ per\ class[/tex]

The y-intercept is [tex]b=\$100[/tex]

so

[tex]y=10x+100[/tex] ----> equation A

Non-Members

The slope is [tex]m=\$15\ per\ class[/tex]

so

[tex]y=15x[/tex] ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

[tex]10x+100 < 15x[/tex]

Solve for x

subtract 10 x both sides

[tex]100 < 15x-10x[/tex]

[tex]100 < 5x[/tex]

Divide by 5 both sides

[tex]20 < x[/tex]

Rewrite

[tex]x > 20[/tex]

therefore

The number of classes must be greater than 20

Part 2) we have

The sum of 8 and 3 times a number is 23.

Let

x ----> the number

Remember that

3 times a number is the same that multiply 3 by the number ----> 3x

so

The sum of 8 and 3 times a number is 23 is the same that

[tex]8+3x=23[/tex]

solve for x

subtract 8 both sides

[tex]3x=23-8[/tex]

[tex]3x=15[/tex]

Divide by 3 both sides

[tex]x=5[/tex]

Part 3) we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost of renting a car for one day

x ----> the number of miles

we have

The slope is [tex]m=\$0.42\ per\ mile[/tex]

The y-intercept is [tex]b=\$36[/tex]

so

[tex]y=0.42x+36[/tex]

For x=78 miles

substitute in the linear equation and solve for y

[tex]y=0.42(78)+36[/tex]

[tex]y=\$68.76[/tex]

Part 4) Let

x ----> Alice's normal hourly rate

we know that

40 hours multiplied by her normal hourly rate plus 10 hours (50 h-40 h) multiplied by 1.5 times her normal hourly rate must be equal to $660

so

The linear equation that represent this situation is

[tex]40x+10(1.5x)=660[/tex]

solve for x

[tex]40x+15x=660[/tex]

[tex]55x=660[/tex]

Divide by 55 both sides

[tex]x=\$12\ per\ hour[/tex]

Part 5) Let

x ----> the cost of one print

we know that

The cost of one print multiplied by 27 prints must be equal to $242.73

so

The linear equation is equal to

[tex]27x=242.73[/tex]

solve for x

Divide by 27 both sides

[tex]x=\$8.99[/tex]

Part 6) we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

Members

The slope is [tex]m=\$7\ per\ class[/tex]

The y-intercept is [tex]b=\$120[/tex]

so

[tex]y=7x+120[/tex] ----> equation A

Non-Members

The slope is [tex]m=\$11\ per\ class[/tex]

so

[tex]y=11x[/tex] ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

[tex]7x+120 < 11x[/tex]

Solve for x

subtract 7x both sides

[tex]120 < 11x-7x[/tex]

[tex]120 < 4x[/tex]

Divide by 4 both sides

[tex]30 < x[/tex]

Rewrite

[tex]x > 30[/tex]

therefore

The number of classes must be greater than 30

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