BLoCK 4
Lesson 22 ~ Expressions and Equations
Write an algebraic expression for each phrase.
1.
the product of nine and y2.
the sum of m and six3.
four less than the product of z and eight4.
two more than the quotient of c and fi veevaluate each expression.
5.
x _ 2 − 9 when x = 306.
6b + 5 when b = −47.
5k − 7n when k = 10 and n = −28.
2 _ 9 m + 1 _ 3 when m = 3determine if the number given is the solution of the equation.
9.
4x + 1 = 9 Is 2 the solution?10.
−3y − 5 = −7 Is 4 the solution?11.
__ m 6 + 5 = 7.3 Is 15 the solution?12.
1 _ 4 h + 2 = 0 Is −8 the solution?Block 4 ~ Review
141
Lesson 23 ~ Solving One-Step Equations
solve each equation using an equation mat or inverse operations. Check your solution.
13.
3x = 2114.
y + 81 = 10715.
__ −4 p = 716.
3.25 = m − 6.2517.
0.2k = 1.118.
− __ 12 5 + x = 1 _ 6Write an algebraic equation for each sentence. solve the equation using an equation mat or inverse operations.
19.
Th e product of x and nine equals thirty-six.20.
Th e quotient of x and two is two-fi ft hs.21.
Th irty-one less than x is negative ten.22.
Th e sum of x and one-half equals thirteen.23.
Kate is thinking of two numbers. Th e sum of the numbers is −8. If one of the numbers is 12, what is the other number? Write an equation and solve it to fi nd the missing number.Lesson 24 ~ Solving Two-Step Equations
solve each equation for the variable. Check your solution.
24.
8x − 9 = 725.
__ h 4 + 3 = −626.
21 = 7 − 2x27.
2m + 6 = 1828.
0.5y + 1.9 = 10.429.
−6x + 14 = 2Write an equation for each statement. solve the problem. Check the solution.
30.
Four times a number x plus eleven is thirty-fi ve. Find the number.31.
Th e number y divided by negative six decreased by seven is eleven. Find the number.32.
Partridge Middle School hosts an ice cream social each month. Th is month, there were eight more than three times as many people at the ice cream social than last month. Th ere were 128 people at the ice cream social this month. Write and solve a two-step equation to determine how many people attended last month’s ice cream social.142
Block 4 ~ ReviewLesson 25 ~ The Distributive Property
use the distributive Property to rewrite each expression without parentheses.
33.
8(x + 10)34.
3(5y − 4)35.
−2(x − 9)solve each equation for the variable. Check the solution.
36.
3(x − 5) = 2137.
−8(x + 4) = 1638.
26 = 2(3x + 1)39.
−5(2x − 9) = −5540.
1 _ 2 (8x + 2) = −341.
77 = −11(x − 2)42.
Three sisters went to the movie theater together on Saturday night. It cost $7.50 for each sister to enter the theater. Each sister spent an equal amount of money at the concession stand. The evening cost the three sisters $37.50.a. Let c represent the amount of money each sister spent at the
concession stand. Write an equation using the Distributive Property to represent this situation.
b. Solve the equation. How much did each sister spend at the concession stand?
Lesson 26 ~ Simplifying Expressions
simplify each algebraic expression.
43.
8 − 7y + 6 + 10y44.
11a + 5d − a − 10a − 7d45.
5(2x + 7) + x − 446.
2(4x + 1) − 7x + 247.
15 + 3(p + 2)48.
13 − 2(x − 6)49.
It takes Owen 40 minutes to get to his best friend’s house. He spends m minutes riding his bike to the bus stop at a rate of 0.2 miles per minute. He gets on the bus and travels the rest of the way at a rate of 0.5 miles per minute. The total distance traveled is represented by the expression 0.2m + 0.5(40 − m).a. Simplify this expression.
b. Owen rides his bike for 16 minutes. Use the expression to determine the total distance to his friend’s house.
Lesson 27 ~ Simplifying and Solving Equations
solve each equation for the variable. Check your solution.
50.
7a + 2a − 4a = −4551.
10y + 9 − 3y + 1 = 5952.
−7 = −3(x + 1) + 2x53.
2 + 1 _ 5 m + __ 10 3 m + 7 = 554.
−52 = 4(x − 8) − 2(x − 5)55.
40 − 2(d + 5) = 20Block 4 ~ Review
143
Lesson 28 ~ Solving Equations With Variables on Both Sides
solve each equation for the variable. Check your solution.
56.
4x + 35 = 11x57.
5p − 10 = 8p + 1458.
25 − 9c = c59.
0.4h + 1 = 16 − 1.1h60.
3 _ 8 x − 2 = 1 _ 8 x + 461.
11 + 4a = a + 562.
Th e local video game rental store has a Frequent Gamers Plan. It costs $30 to join and each video game rental for members costs $2. Non-members pay a rental fee of $3.50 per rental. Let g represent the total number of video games rented.a. Write an expression to represent the total cost for g rentals by a member.
b. Write an expression to represent the total cost for g rentals by a non-member.
c. Set the two expressions equal to each other and solve the equation to fi nd the number of rentals when both plans cost the same amount.
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usi n e s sNate started a business selling coff ee and muffi ns at the local senior center.
He spent $250 for a coff ee cart and also paid $500 to rent a space for his cart at the senior center for one year. He calculated that he makes a profi t of $0.75 for each cup of coff ee and $1.25 for each muffi n he sells. Help evaluate Nate’s business plan. Show all work.
1.
If Nate were to only sell coff ee and no muffi ns, how many cups of coff ee would he need to sell in one year to break even (cover his expenses)?2.
If Nate were to sell the same amount of coff ee and muffi ns, about how many of each would he need to sell to break even?3.
Nate estimates he will make a profi t of about $945 this year.a. If he only sells coff ee, how many cups will he need to sell to reach his estimate?
b. If he only sells muffi ns, how many muffi ns will he need to sell to reach his estimate?
c. If he sells both muffi ns and coff ee, determine two diff erent combinations of coff ee and muffi ns that would allow him to reach a profi t of $945.
4.
Design your own business. What would your expected start-up costs be? What products would you sell? How much would you hope your profi t would be for each product you would sell? How many of each product would you need to sell to break even?144
Block 4 ~ Reviewr
AchelleA
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regonI am the director for an international adoption agency. I match orphaned children from all over the world with adoptive parents. Some adoption agencies work only with adoptions of children in the Unites States. Other agencies help families adopt children from other countries. I travel to other countries, such as India and Guatemala, to escort children to their new families.
When looking at children who will be coming up for adoption, I look at their growth measurements such as how big they are, how quickly they are growing, and how tall they are. I chart a child’s growth on a graph. I use math
to determine what percentile they fall in for each measurement. Because I work with countries that use the metric system, I convert metric measurements to customary measurements. This helps parents in the United States better understand how healthy a child is.
A person must have a degree in a related field such as social work or sociology to work on adoptions. It is also a good idea for adoption workers to get some international experience. Visiting other countries helps a person know how that culture works. This is very helpful when adopting from that country. A person just entering the field of adoptions can expect to make $26,000 - $29,000 a year. That salary varies based on how much experience the person has.
Working as an adoption agent can be very difficult work. Sometimes I come across sad circumstances. However, this job is very rewarding because I can unite a child from a poor situation with a new, loving family.