Intermediate Algebra Chapter 4 Exam Review

Solve the following linear system by graphing.

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1.

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Solve the follovwng linear system by graphing.

y=-x+4

......

/ \ f \ / 1 :

" J f 1 } , J /

/ \ / \

} j

/ i ..... !

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\

. J

2. + 3>; = -6

Solve the following linear systems by substitution.

2x-y = 2 2t\ -ZuVl\=Z 4.

1

1 I

I \ I i

i ?^ J !

\ i

!

1 1 1 i

6.

Solve the following linear systems by elimination.

^ - i t 2 . \f\\i-.iX\A^^^

3x + 43; = 11 ^J^h^^f-^

l 3

8.

\lc solitiioii

2x + l>y-z = - \

10. x + 23 + z = 4 ,

6x-8y + 2z = S'^

Solve the following linear systems by the method of your choice.

11. . .7. Pi ^v/t34-M

4 ^ 3 5 ^ ^ - x + ->' = l l

,4' 2"^

12. I ^ ^ l-

S 3 '

- 6 i - ~ Z 5

3 T ^

U (f- ^

13. Say you sold boxes of peanut butter cookies for $2.50 and boxes of chocolate chip cookies for $3.25. One day you sold 47 boxes and made $134. How many boxes of.Bacti did you sell?

Equadons: ^. I f f - ^ ^ = M ' ^ J t

14. The other day I went to Staples to buy some office supphes. I bought 2 pens and 3 binders, which together cost me $9.75. My friend bought 3 of the same pens and 2 of the same binders, and it cost her $9.00. What is the cost for a single binder and the cost for a single pen?

Let X - \\i (Citc\^ ( i j - f i ^ .

Let - \ ( M i.C.A 4 \

5 -

15. A rowing team, while practicmg, rowed an average of 17.9 miles per hour with the current and 10.7 miles per hour against the current. Determine the team's rowing speed in shll water and the speed of the current.

Let ii^ = .)\>^tAe^ ^vc ( U u ( A \ ( ^ ^ j ^

Equations:

) i 3

16. You invested $8000 in two funds paying 2% and 5% annual interest. At the end of the year, the interest from the 5% investment exceeded the interest from the 2% investment by $85. How much money was invested at each rate?

Let X = \x<LxiM^^w:'krA?^ n

Let x \ >.MXvi>^ S n V t W c V A \

Equations: d,, X\\A=K^L±J^^Y'^ A.^m^' ^^^^

17. The manager of a gardenmg' center needs to mix a plant food that is 13% nitrogen with one that is 18% nitrogen to obtain 50 gallons of a plant food that is 16% nitrogen. How many gallons of each of the plant foods must be used?

L e t X = .

L e t i ^ = .

Equations; - 5 C . - X

18. A company that produces'an^ sells radios has an annual cost of producing radios at $10,000 with a $30 production cost for each radio produced. The annual cost for producing the radios, C(x), is the function C (x) = 30x + 10000 , where x is the number of radios produced. The annual revenue of selling the radios is $50 for each radio sold. The annual revenue, R(x), is the function R{x) = 50x, where x is the number radios sold. Solve the system of equations to detennine the number of radios that must be produced and sold to break even. What will be the cost and revenue for producing and selling that many radios?

100 200 300 4(K) Sm 600 7(K)

Radios Produced and Sold

19. Three kmds of tickets for a Soggy Bottom Boys concert are available: up-front, mam-floor, and balcony. The most expensive tickets, the up-front tickets, are twice as expensive as balcony tickets. Balcony tickets are $10 less than main-floor tickets and $30 less than up-front tickets. Determine the price of each kind of ticket? r ^ / C ^ ' " Let = 9% .. iXD"\TC > ^ ^ Let j j ^ = _ p t : ^ d \m\)\v Let

Equations: (I' X = K - 2 C ) C r - 3 d S

i-yo

20. The largest angle of a triangle has a measure that is less than three times the measure of the second smallest angle. The measure of the smallest angle is equal to the difference between the measure of the largest angle and twice the measure of the second smallest angle. Determine the measures of the three angles of the triangle. Let j<_= \y^k<m^^ gj\A S\iY% A Let Let

Equations:

21. At the local bar 5 beers, 3 mixed drinks, and 2 shooters are sold for $54; 4 beers, 2 mixed drinks, and 3 shooters are sold for $46; and I beer , 4 mixed drinks, and 1 shooter are sold for $^,. What is the price of 1 beer, 1 mixed drink, and 1 shooter sold individually? (j vic! - '•S(^)-tdi^)+/iHj ~ S ^ V - " ^ Let X = Let U = _ t l £ j 2 Let j =

Equation,: SK ^^^If^ = , , , /

- 5

22. A garden store owner needed to keep track of the number of 15-pound bags, 20-pound bags, and 30-pound bags of soil he sold during the week, which sell for $7.50, $9, and $12.50, respectively. He completely forgot to keep track, but he knew he could figure it out. The register tape revealed that a total of 22 bags were sold, which brought in a total of $213.50. He also could tell from the depleted dirt pile that he sold a total of 480 pounds of dirt. How many bags of each size did the owner sell? Let Let Let r = l U u ^ U V r ^ i V H b b c V ^ .

Equations: (ij \cr^^^ iQx^ d C % ^ ^ fiO V

til some of the money, he purchased a f) 23. A person invested $15,000 among three different investments. Witii some of the money, he purchased a municipal bond paying 5.5% simple interest. He invested twice the amount of money that he paid for the municipal bond in a certificate of deposit paying 4.5% simple interest. He placed the balance of the money in a money market account paying 3.75% simple interest. If the total interest for 1 year was $692.50, how much was placed in each account? /T^TTI ' t\. V

Let

24. A 14% solution, an 18% solution, and a 36% solution of saline are to be mixed to get 12 titers of a 22% solution. How many liters of each must be mixed i f the volume of the 36% solution must be 2 liters less than twice the volume of the 14% solution? y-f Let A Let Let

Equations: ^

)t y ^

Solve the following system of linear inequalities by graphing.

2x + y> 2 25.

1

Solve the following system of linear inequalities by graphing.

.2x-6y > 6 26.

x>-2

Solve the following system of linear inequalities by graphing.

X<1 11. y>-3

sdaikn

Solve the following system of linear inequalities by graphing. /•i-^^v'^ 'ii' V \ A y / ^

28.

x\>2 ^

X>Z. or -X.>i

X>Z. or

Solve the fol lowing system of linear inequalities by graphing.

29.

A ' + 2 > 4

> < 4 ^'

X^Z or X, <-fc Solve the following system of linear inequalities by graphing.

30,