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Chapter 2 5 Glencoe Algebra 1

Study Guide and InterventionWriting Equations

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Write Equations Writing equations is one strategy for solving problems. You can use a variable to represent an unspecified number or measure referred to in a problem. Then you can write a verbal expression as an algebraic expression.

Translate each sentence into an equation or a formula.

a. Ten times a number x is equal to 2.8 times the difference y minus z.10 × x = 2.8 × ( y - z)The equation is 10x = 2.8( y - z).

b. A number m minus 8 is the same as a number n divided by 2.m - 8 = n ÷ 2The equation is m - 8 = n −

2 .

c. The area of a rectangle equals the length times the width. Translate this sentence into a formula.Let A = area, ℓ = length, and w = width.Formula: Area equals length times width. A = ℓ × wThe formula for the area of a rectangle is A = ℓw.

Use the Four-Step Problem-Solving Plan.POPULATION The population of the United States in July 2007 was about 301,000,000, and the land area of the United States is about 3,500,000 square miles. Find the average number of people per square mile in the United States.

Step 1 Explore You know that there are 301,000,000 people. You want to know the number of people per square mile.

Step 2 Plan Write an equation to represent the situation. Let p represent the number of people per square mile.

3,500,000 × p = 301,000,000Step 3 Solve 3,500,000 × p = 301,000,000.

3,500,000p = 301,000,000 Divide each side by

p = 86 3,500,000.

There are 86 people per square mile.Step 4 Check If there are 86 people per square

mile and there are 3,500,000 square miles, 86 × 3,500,000 = 301,000,000. The answer makes sense.

ExercisesTranslate each sentence into an equation or formula.

1. Three times a number t minus twelve equals forty.

2. One-half of the difference of a and b is 54.

3. Three times the sum of d and 4 is 32.

4. The area A of a circle is the product of π and the radius r squared.

5. WEIGHT LOSS Lou wants to lose weight to audition for a part in a play. He weighs 160 pounds now. He wants to weigh 150 pounds.

a. If p represents the number of pounds he wants to lose, write an equation to represent this situation.

b. How many pounds does he need to lose to reach his goal?

Example 2Example 1

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Chapter 2 6 Glencoe Algebra 1

Study Guide and Intervention (continued)

Writing EquationsWrite Verbal Sentences You can translate equations into verbal sentences.

Translate each equation into a sentence.

a. 4n - 8 = 12.

4n - 8 = 12Four times n minus eight equals twelve.

b. a2 + b2 = c2

a2 + b2 = c2

The sum of the squares of a and b is equal to the square of c.

ExercisesTranslate each equation into a sentence.

1. 4a - 5 = 23 2. 10 + k = 4k

3. 6xy = 24 4. x2 + y2 = 8

5. p + 3 = 2p 6. b = 1 − 3 (h - 1)

7. 100 - 2x = 80 8. 3(g + h) = 12

9. p2 - 2p = 9 10. C = 5 − 9

(F - 32)

11. V = 1 − 3

Bh 12. A = 1 − 2

hb

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Example

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Chapter 2 8 Glencoe Algebra 1

PracticeWriting Equations

Translate each sentence into an equation.

1. Fifty-three plus four times b is as much as 21.

2. The sum of five times h and twice g is equal to 23.

3. One fourth the sum of r and ten is identical to r minus 4.

4. Three plus the sum of the squares of w and x is 32.

Translate each sentence into a formula.

5. Degrees Kelvin K equals 273 plus degrees Celsius C.

6. The total cost C of gas is the price p per gallon times the number of gallons g.

7. The sum S of the measures of the angles of a polygon is equal to 180 times the difference of the number of sides n and 2.

Translate each equation into a sentence.

8. r - (4 + p) = 1 − 3 r 9. 3 −

5 t + 2 = t

10. 9(y2 + x) = 18 11. 2(m - n) = x + 7

Write a problem based on the given information.

12. a = cost of one adult’s ticket to zoo 13. c = regular cost of one airline ticketa - 4 = cost of one children’s ticket to zoo 0.20c = amount of 20% promotional discount

2a + 4(a - 4) = 38 3(c - 0.20c) = 330

14. GEOGRAPHY About 15% of all federally-owned land in the 48 contiguous states of the United States is in Nevada. If F represents the area of federally-owned land in these states, and N represents the portion in Nevada, write an equation for this situation.

15. FITNESS Deanna and Pietra each go for walks around a lake a few times per week. Last week, Deanna walked 7 miles more than Pietra.

a. If p represents the number of miles Pietra walked, write an equation that represents the total number of miles T the two girls walked.

b. If Pietra walked 9 miles during the week, how many miles did Deanna walk?

c. If Pietra walked 11 miles during the week, how many miles did the two girls walk together?

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Chapter 2 9 Glencoe Algebra 1

Word Problem PracticeWriting Equations

1. HOUSES The area of the Hartstein’s kitchen is 182 square feet. This is 20% of the area of the first floor of their house. Let F represent the area of the first floor. Write an equation to represent the situation.

2. FAMILY Katie is twice as old as her sister Mara. The sum of their ages is 24. Write a one-variable equation to represent the situation.

3. GEOMETRY The formula F + V = E + 2 shows the relationship between the number of faces F, edges E, and vertices V of a polyhedron, such as a pyramid. Write the formula in words.

Face

Vertex Edge

4. WIRELESS PHONE Spinfrog wireless phone company bills on a monthly basis. Each bill includes a $29.95 service fee for 1000 minutes plus a $2.95 federal communication tax. Additionally, there is a charge of $0.05 for each minute used over 1000. Let m represent the number of minutes over 1000 used during the month. Write an equation to describe the cost p of the wireless phone service per month.

5. TEMPERATURE The table below shows the temperature in Fahrenheit for some corresponding temperatures in Celsius.

Celsius Fahrenheit

-20° -4°

-10° 14°

0° 32°

10° 50°

20° 68°

30° 86°

a. Write a formula for converting Celsius temperatures to Fahrenheit temperatures.

b. Find the Fahrenheit equivalents for 25ºC and 35ºC.

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