Question

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?

Answer 1

Answer:

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

Part 2) see the explanation

Part 3) $\ 68.76$

Part 4) $\ 12\ per\ hour$

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

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

$y=mx+b$

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 $m=\ 10\ per\ class$

The y-intercept is $b=\ 100$

so

$y=10x+100$ ----> equation A

Non-Members

The slope is $m=\ 15\ per\ class$

so

$y=15x$ ----> 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

$10x+100 < 15x$

Solve for x

subtract 10 x both sides

$100 < 15x-10x$

$100 < 5x$

Divide by 5 both sides

$20 < x$

Rewrite

$x > 20$

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

$8+3x=23$

solve for x

subtract 8 both sides

$3x=23-8$

$3x=15$

Divide by 3 both sides

$x=5$

Part 3) we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

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 $m=\ 0.42\ per\ mile$

The y-intercept is $b=\ 36$

so

$y=0.42x+36$

For x=78 miles

substitute in the linear equation and solve for y

$y=0.42(78)+36$

$y=\ 68.76$

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

$40x+10(1.5x)=660$

solve for x

$40x+15x=660$

$55x=660$

Divide by 55 both sides

$x=\ 12\ per\ hour$

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

$27x=242.73$

solve for x

Divide by 27 both sides

$x=\ 8.99$

Part 6) we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

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 $m=\ 7\ per\ class$

The y-intercept is $b=\ 120$

so

$y=7x+120$ ----> equation A

Non-Members

The slope is $m=\ 11\ per\ class$

so

$y=11x$ ----> 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

$7x+120 < 11x$

Solve for x

subtract 7x both sides

$120 < 11x-7x$

$120 < 4x$

Divide by 4 both sides

$30 < x$

Rewrite

$x > 30$

therefore

The number of classes must be greater than 30