30 PIONTS Sam walked for 30 minutes more than Jessica. Courtney walked twice as long as Sam. Courtney walked for 80 minutes. The equation 2(x + 30) = 80 describes this situation.

What does x represent?

Answer choices-

the number of minutes that Jessica walked

The number of minutes that Sam walked

The number of minutes that Courtney walked

The total number of minutes the girls walked combined

a. the number of minutes jessica walked

Step-by-step explanation:

because it doesnt necessarily tell us how much minutes she walked.

EXAMPLE

Pete bought a shirt on sale for $

18

18, which is one-half the original price. What was the original price of the shirt?

Solution:

Step 1. Read the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the Internet.

In this problem, do you understand what is being discussed? Do you understand every word?

Step 2. Identify what you are looking for. It’s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!

In this problem, the words “what was the original price of the shirt” tell you what you are looking for: the original price of the shirt.

Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.

Let

p

=

p= the original price of the shirt

Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.

The top line reads:

Step 5. Solve the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers.

Write the equation.

18

=

1

2

p

18=12p

Multiply both sides by 2.

2

⋅

18

=

2

⋅

1

2

p

2⋅18=2⋅1Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.

Let

p

=

p= the original price of the shirt

Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.

The top line reads:Step 5. Solve the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers.

Write the equation.

18

=

1

2

p

18=12p

Multiply both sides by 2.

2

⋅

18

=

2

⋅

1

2

p

2⋅18=2⋅12p

Simplify.

36

=

p

36=pStep 6. Check the answer in the problem and make sure it makes sense.

We found that

p

=

36

p=36, which means the original price was

$36

$36. Does

$36

$36 make sense in the problem? Yes, because

18

18 is one-half of

36

36, and the shirt was on sale at half the original price.Step 7. Answer the question with a complete sentence.

The problem asked “What was the original price of the shirt?” The answer to the question is: “The original price of the shirt was

$36

$36.”

If this were a homework exercise, our work might look like this:

The top reads,

TRY IT

The coordinates of U is (3, -3)

Step-by-step explanation:

The given vertices of the parallelogram MULE are;

M(-2, -4), L(0, 7), E(1, 0)

We have;

L(0, 7) and E(1, 0) are the 'y' and x-intercepts of the side LE of the parallelogram MULE

The slope of LE = (0 - 7)/(1 - 0) = -7

With segment MU parallel to LE, we have;

The slope of MU = The slope of LE = -7

The equation of the line segment MU in point and slope form is therefore presented as follows;

y - (-4) = -7 × (x - (-2))

y + 4 = -7·x - 14

y = -7·x - 18

∴ The equation of the line segment MU is 'y = -7·x - 18'

The slope of the line segment ME = (0 - (-4))/(1 - (-2)) = 4/3

For the parallelogram MULE, we have;

The slope of the line segment ME = The slope of the line segment UL

∴ The slope of the line segment UL = 4/3

The equation of the line segment UL in point and slope form is therefore presented as follows;

y - 7 = (4/3)·(x - 0)

∴ y = 4·x/3 + 7

The equation of the line segment UL is 'y = 4·x/3 + 7'

The point 'U' is given by finding the value of 'y' that satisfies the equations of the line segments MU and UL as follows;

The equation for MU is 'y = -7·x - 18'

The equation for UL is 'y = 4·x/3 + 7'

At vertex point 'U', we have;

y = -7·x - 18 = y = 4·x/3 + 7

-7·x - 18 = 4·x/3 + 7

7·x + 4·x/3 = -18 - 7 = -25

(21·x + 4·x)/3 = 25·x/3 = -25

25·x/3 = -25

∴ x = -25 × 3/25 = -3

The x-axis coordinate of the point 'U', x = -3

y = 4·x/3 + 7

∴ y = 4 × (-3)/3 + 7 = -4 + 7 = 3

y = 3

The y-axis coordinate of the point 'U', y = -3

The coordinates of the vertex 'U', (x, y) = (3, -3)