# linear equations and inequality

Complete each problem show work and ad graphs as needed

John spent 1/3 of his inheritance on loose women, 1/5 on expensive cigars, and 3/10 on liquor. He invested the rest in lottery tickets. What percent of his inheritance went to lottery tickets?

Evaluate the expression:

-(2 - 3)4

Fred and Ethel are florists. They are making rose and lilly of the valley bouquets for Valentine's day. Fred can make 3 bouquets per hour, but Ethel can only make 2 bouquets per hour. Working together, how many bouquets per hour do they make?

Solve the equation. Remember to show your work and check your answer:

3(q+5) - q = 29

Solve the equation. Remember to show your work and check your answer:

28 + 31.7 d= d - 12

Solve the equation for n.

9n - m + 7 = 0

Solve the indicated inequality. Give your answer in interval notation:

1 + 0.94x > 1.26

Mary Jo is looking to buy a new car. She has $22,,000 to spend. If the sales tax in her town is 6%, and registration is $450, in what price range should she shop for the car?

Find the slope and the y intercept of the equation 5x + 12 y = 60

Determine whether the two given lines are parallel, perpendicular, or neither.

5x + 8y = 23

y = 2 + 8/5 x

Find the equation of the line that goes through the points (1, -2) and (2, 5)

Solve by using any method

4x + y = 48

x - 3y = - 19

Solve the inequality. Write your answer in interval notation.

3|12 - 4x| - 9 < 11

Joey received plenty of Batman and Spiderman action figures at his birthday party. He received 11 of these action figures all together. When he returned them all to the store to exchange for a giant Yoda, he received $71. If Batmen sell for $5 each and Spidermen sell for $7 each, how many of each did he receive?

The inequality 1,200b + 2,200y < 50,000 describes the number of mountain bikes and youth programs that a police chief can budget for the season (b = bikes, and y = youth programs). Can the chief afford 25 mountain bikes and 15 youth programs?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please see the attached file.

Complete each problem show work and ad graphs as needed

John spent 1/3 of his inheritance on loose women, 1/5 on expensive cigars, and 3/10 on liquor. He invested the rest in lottery tickets. What percent of his inheritance went to lottery tickets?

The total is 1, then amount left for lottery tickets is

So 1/6 or 16.67% of his inheritance went to lottery tickets.

Evaluate the expression:

-(2 - 3)4 =

Fred and Ethel are florists. They are making rose and lilly of the valley bouquets for Valentine's day. Fred can make 3 bouquets per hour, but Ethel can only make 2 bouquets per hour. Working together, how many bouquets per hour do they make?

bouquets per hour they can make together.

Solve the equation. Remember to show your work and check your answer:

3(q+5) - q = 29

Check:

Solve the equation. Remember to show your work and check your answer:

28 + 31.7 d= d - 12

Check:

Solve the equation for n.

9n - m + 7 = 0

Solve the indicated inequality. Give your answer in interval notation:

1 + 0.94x > 1.26

In interval notation:

Mary Jo is looking to buy a new car. She has $22,,000 to spend. If the sales tax in her town is 6%, and registration is $450, in what price range should she shop for the car?

The car price is x. the tax is 6%x. The total for the car is

She should shop the car for less than $20330.19

Find the slope and the y intercept of the equation 5x + 12 y = 60

The equation can be rearranged as

So the slope is -5/12, the y-intercept is 5.

Determine whether the two given lines are parallel, perpendicular, or neither.

5x + 8y = 23

y = 2 + 8/5 x

The first one

The slope is -5/8.

The second one , the slope is 8/5

Since the product of two slopes is . So the two lines are perpendicular.

When the slopes are the same, the lines are parallel to each other.

Find the equation of the line that goes through the points (1, -2) and (2, 5)

The slope is

Now the equation is y=7x+b

Substitute (1, -2) into the equation

So the line is

Solve by using any method

4x + y = 48 (1)

x - 3y = - 19 (2)

Using the substitution method

From (2) we have x=3y-19, substitute it into (1)

Then

Solve the inequality. Write your answer in interval notation.

3|12 - 4x| - 9 < 11

Overall,

In interval notation:

Joey received plenty of Batman and Spiderman action figures at his birthday party. He received 11 of these action figures all together. When he returned them all to the store to exchange for a giant Yoda, he received $71. If Batmen sell for $5 each and Spidermen sell for $7 each, how many of each did he receive?

Assume he received x Batman, y spiderman.

From (1) y=11-x

Substitute into (2)

So y=11-x=11-3=8

He received 3 Batman, 8 Spiderman.

The inequality 1,200b + 2,200y < 50,000 describes the number of mountain bikes and youth programs that a police chief can budget for the season (b = bikes, and y = youth programs). Can the chief afford 25 mountain bikes and 15 youth programs?

So the chief cannot afford 25 bikes and 15 youth programs.

Â© BrainMass Inc. brainmass.com October 5, 2022, 5:14 pm ad1c9bdddf>https://brainmass.com/math/linear-algebra/linear-equations-inequality-94701