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Step by Step Algebra Solutions

Solve 2(x-4)=2[x-3(x-1)+2]

Solve x-2 - x+5 =5x-2
3 6 9

The cell phone service for the CEO of a small company is $39.99 a month plus $0.10 per minute for long distance. In a month when the company's phone bill was $75.19, how many minutes of long distance did the CEO use? Set up an equation and solve. Show all work to receive full credit.

Equation:

The equation d=rt represents the formula for total distance traveled. The distance traveled, d, is equal to the rate of travel, r, multiplied by the time of travel, t. Use this formula to help solve the following problem.

Two runners, Jay and Ben, start at the same time from opposite ends of an 8-mile jogging trail and begin running toward each other. Jay is running at the rate of 5 mph, and Ben is running at a rate of 7 mph. How long, in minutes, after they start will Jay and Ben meet?

A. Who will have traveled the longer distance?

B. When they meet, what is the combined distance Jay and Ben will have traveled?

C. What equation represents this situation?

D. Solve the equation; show work your here:

E. How long, in minutes, did it take for Jay and Ben to meet?

5. Solve the following two equations separately: 3x=2x+x+2 and 2(x-1)=4x-2

Show work for solving 3x=2x+x+2 here:

Show work for solving 2 (x-1)=4x-2 here:

Explain the difference between the two solutions; it must be detailed to receive full credit:

6. A clothing store may reduce the regular price of a product because the clothes are damaged, odd sizes, or discontinued items. The discount, or markdown, is the amount by which the store reduces the regular price of a product. The percent discounted is called the discount rate and is usually expressed as a percent of the original selling price. Taking the regular price and subtracting the discount calculates the sale price. The formula s=R-rR can be used to help find the sale price. The sale price, S, is equal to the regular price, R, minus the discount rate, r, multiplied by the regular price, R (Aufmann, Vernon, & Lockwood, 2006).

Using the aforementioned information, solve the following problems.

A. A pair of shoes that are currently selling for a price of $89.99 are going to be marked down 20% for the spring sale. Use the sale price formula to find the new
price of the shoes. Round to the nearest cent.

Set up equation:

Show work here:

Sale price of shoes:

B. A suit coat that is marked down 35% has a sale price of $292.50. Use the sale price
formula to find the regular price of the suit coat. Round to the nearest cent.

Set up equation:

Show work here:

Regular price of the suit coat:

C. Using the formula S=R-rR , find another formula that represents the discount
rate. (Hint: Solve for r.)

Discount rate formula:

D. A prom dress with a regular price of $395 is on sale for $280. Find the discount rate;
round to the nearest tenth of a percent.

Show work here:

Discount rate:

Solution Preview

Hi there!

Here are the step-by-step solutions:

solve 2(x-4)=2[x-3(x-1)+2]
Distribute the 2 on the left side:
2x - 8 = 2[x-3(x-1)+2]
Distribute the 2 on the right side:
2x - 8 = 2x - 6(x-1) + 4
Distribute the 6 on the right side:
2x - 8 = 2x - 6x + 6 + 4
Combine terms on the right side:
2x - 8 = -4x + 10
Add 8 to each side:
2x = -4x + 18
Add 4x to each side:
6x = 18
Divide each side by 6:
x = 3

solve x-2 - x+5 =5x-2
3 6 9

We need a common denominator. Let's use 18. Multiply the first term by 6/6, the second term by 3/3, and the final term by 2/2:
6(x-2) - 3(x+5) = 2(5x-2)
18 18 18

Multiply everything by 18:
6(x-2) - 3(x+5) = 2(5x-2)
Distribute each term:
6x - 12 - 3x - 15 = 10x - 4
Combine like terms on the left:
3x - 27 = 10x - 4
Add 4 to each side:
3x - 23 = 10x
Subtract 3x from each side:
-23 = 7x
Divide by 7:
x = -23/7

The cell phone service for the CEO of a small company is $39.99 a month plus $0.10
per minute for long distance. In a month when the company's phone bill was $75.19,
how many minutes of long distance did the CEO use? Set up an equation and solve.
Show all work to receive full credit.

Equation:
cost = 39.99 + 0.10*minutes
Plug in what we know:
75.19 = 39.99 + 0.10m
Subtract 39.99:
35.2 = 0.10m
Multiply each side by 10:
m = 352 minutes

The equation d=rt represents the formula for total distance ...

Solution Summary

This solution shows how to solve the algebra problems with explanation of each step.

$2.19