Question 1

Solve the problem.
-An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highwaydriving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?
A)153 mi
B)147 mi
C)132 mi
D)168 mi

Accepted Answer

The car traveled 15.5 * 18 = 279 miles in the city and 15.5 * 21 = 325.5 miles on the highway. Since the total trip was 300 miles, the car traveled 279 - 300 = 153 miles in the city.

Question 2

Solve the system of equations. If the system has no solution, say that it is inconsistent.
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A)x = 0, y = 0; (0, 0)
B)x = -9, y = -5; (-9, -5)
C)x = 0, y = -14; (0, -14)
D)inconsistent

Accepted Answer

The answer of Solve the system of equations. If the...

Question 3

Write the word or phrase that best completes each statement or answers the question.
-A tea shop owner is mixing a blend of two teas, one of which costs $6.50 per pound, the other costing $4.00per pound. The owner wants to have 20 pounds of a mixture that will sell for $5.50 per pound. How muchof each type of tea should be used?

Accepted Answer

The answer of Write the word or phrase that best...

Question 4

Write the word or phrase that best completes each statement or answers the question.
-A store has a sale on workout gear. Mark bought three pairs of shorts and three T-shirts for $70.35 (beforetax). Later, he went back and bought two more pairs of shorts and four more T-shirts for $63.90 (beforetax). How much did the shorts and T-shirts cost?

Accepted Answer

The answer of Write the word or phrase that best...

Question 5

Solve the problem.
-A tour group split into two groups when waiting in line for food at a fast food counter. The first groupbought 7 slices of pizza and 4 soft drinks for $31.35. The second group bought 5 slices of pizza and 5 softdrinks for $26.40. How much does one slice of pizza cost?
A)$3.41 per slice of pizza
B)$1.87 per slice of pizza
C)$2.91 per slice of pizza
D)$2.37 per slice of pizza

Accepted Answer

Let x be the cost of a slice of pizza and y be the cost of a soft drink.For the first group:7x + 4y = 31.35For the second group:5x + 5y = 26.40Solving the system of equations:7x + 4y = 31.355x + 5y = 26.40Multiply the second equation by -4:-20x - 20y = -105.60Add the two equations:-13x - 16y = -74.25Divide by -13:x = 5.67Substitute x = 5.67 into the first equation:7(5.67) + 4y = 31.3540.09 + 4y = 31.354y = -8.74y = -2.185Therefore, the cost of a slice of pizza is $5.67.

Question 6

Solve the system of equations by elimination.
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A)x = 12, y = -4; (12, -4)
B)x = -12, y = 3; (-12, 3)
C)x = -12, y = 7; (-12, 7)
D)x = -4, y = 12; (-4, 12)

Accepted Answer

The answer of Solve the system of equations by elimination.
-
A)x...

Question 7

Write the word or phrase that best completes each statement or answers the question.
-The perimeter of a parking lot is 500 yards. Find the dimensions of the lot if the length is 50 yards morethan three times the width.

Accepted Answer

The answer of Write the word or phrase that best...

Question 8

Solve the system of equations. [Hint: Let  , and solve for u and v. Then let 
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the system of equations. [Hint: Let...

Question 9

Solve the system of equations by elimination.
-
A)x = 18, 
B)x = 16, 
C)x = -18, 
D)x = -16,

Accepted Answer

The answer of Solve the system of equations by elimination.
-
A)x...

Question 10

Solve the system of equations by elimination.
-
A)x = 10, y = -3; (10, -3)
B)x = -3, y = 10; (-3, 10)
C)x = -10, y = 3; (-10, 3)
D)x = 3, y = -10; (3, -10)

Accepted Answer

The answer of Solve the system of equations by elimination.
-
A)x...

Question 11

Write the word or phrase that best completes each statement or answers the question.
-A boat on a river goes 77 miles downstream in 2 hours and 45 minutes. The return trip takes 3 hours and30 minutes. If the boatʹs speed is the same in each direction, find the speed of the boat and the speed of thecurrent.

Accepted Answer

The answer of Write the word or phrase that best...

Question 12

Solve the problem.
-A flat rectangular piece of aluminum has a perimeter of 58 inches. The length is 7 inches longer than thewidth. Find the width.
A)11 in.
B)18 in.
C)25 in.
D)29 in.

Accepted Answer

The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. Given that the length is 7 inches longer than the width, we can express the length as l = w + 7. Substituting this into the perimeter formula gives us 58 = 2(w + 7) + 2w. Simplifying, we get 58 = 4w + 14, leading to 44 = 4w, and thus w = 11 inches.

Question 13

Write the word or phrase that best completes each statement or answers the question.
-Jaya has $16,000 to invest. She invests part of it in an account paying 6% simple interest and the rest in anaccount paying 7% simple interest. If her annual income is $1080, how much does she have invested ineach account?

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

Solve the system of equations by elimination.
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A)x = -4, y = 0; (-4, 0)
B)x = 4, y = 0; (4, 0)
C)x = 0, y = -4; (0, -4)
D)x = 0, y = 4; (0, 4)

Accepted Answer

The answer of Solve the system of equations by elimination.
-
A)x...

Question 15

Solve the system of equations by elimination.
-
A)x = 8, y = -8; (8, -8)
B)x = -8, y = 8; (-8, 8)
C)x = 12, y = -12; (12, -12)
D)x = -2, y = 8; (-2, 8)

Accepted Answer

The answer of Solve the system of equations by elimination.
-
A)x...

Question 16

Solve the problem.
-The Family Fine Arts Center charges $22 per adult and $14 per senior citizen for its performances. On arecent weekend evening when 571 people paid admission, the total receipts were $9,378. How many whopaid were senior citizens?
A)398 senior citizens
B)173 senior citizens
C)308 senior citizens
D)263 senior citizens

Accepted Answer

Let x be the number of senior citizens. Then, the number of adults is 571 - x.The total receipts are:22(571 - x) + 14x = 9,378Simplifying:12,542 - 22x + 14x = 9,378-8x = -3,164x = 398Therefore, there were 398 senior citizens.

Question 17

Solve the problem.
-A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and thetheater collected $272.00 at the end of the day, how many of them were adults?
A)24 adults
B)10 adults
C)16 adults
D)29 adults

Accepted Answer

The problem can be solved using a system of equations. Let x be the number of adults and y be the number of children. We have two equations: x + y = 40 (total number of people) and 8x + 5y = 272 (total amount collected). Solving these equations simultaneously, we find x = 24, meaning there were 24 adults.

Question 18

Solve the problem.
-A retired couple has $180,000 to invest to obtain annual income. They want some of it invested in safeCertificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 11% per year. Howmuch should they invest in each to realize exactly $17,300 per year?
A)$130,000 at 11% and $50,000 at 6%
B)$130,000 at 6% and $50,000 at 11%
C)$120,000 at 6% and $60,000 at 11%
D)$140,000 at 11% and $40,000 at 6%

Accepted Answer

Let x be the amount invested in CDs at 6% and y be the amount invested in AA bonds at 11%. We have two equations: x + y = 180,000 (total investment) and 0.06x + 0.11y = 17,300 (total income). Solving these equations simultaneously gives x = 50,000 and y = 130,000, which corresponds to choice A.

Question 19

Solve the problem.
-The Paperback Trader is a book store that takes in used paperbacks for 20% of their cover price and sellsthem for 50% of their cover price. Pat brings in a stack of 17 paperback books to trade and gets $13.73credit. Some of the books had a cover price of $5.98, the rest $2.98. She wants to get some Tom Clancybooks having a cover price of $5.98. How many $5.98 books did she bring in and how many Clancy bookscan she get without paying any additional cash?
A)6 $5.98 books, 4 Clancy books
B)11 $5.98 books, 2 Clancy books
C)6 $5.98 books, 5 Clancy books
D)6 $5.98 books, 2 Clancy books

Accepted Answer

The store buys books for 20% of their cover price and sells them for 50% of their cover price. Pat received $13.73 for her books, which means she traded them in at 20% of their cover price. If x is the number of $5.98 books and y is the number of $2.98 books, the equation based on the trade-in value is 0.20(5.98x + 2.98y) = 13.73. Since Pat brought in a total of 17 books, we also have the equation x + y = 17. Solving these equations simultaneously would give us the number of books of each type she brought in. Without solving these equations explicitly here, we can deduce the correct answer based on the given options and the fact that Pat wants to buy Tom Clancy books priced at $5.98 each, for which she will use her credit. Since she buys them at 50% of the cover price, each Clancy book costs her 0.50 * 5.98 = $2.99. The correct answer must account for both the number of books she brought in and the number she can buy without additional cash, considering the trade-in and selling prices.

Question 20

Solve the system of equations by elimination.
-
A)x = 10, y = 10; (10, 10)
B)x = 0, y = 10; (0, 10)
C)x = 10, y = 0; (10, 0)
D)x = 0, y = 0; (0, 0)

Accepted Answer

The answer of Solve the system of equations by elimination.
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A)x...

Quiz 8: Systems of Equations and Inequalities

Solve the problem. -An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highwaydriving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?

Solve the system of equations. If the system has no solution, say that it is inconsistent. -

Solve the problem. -A tour group split into two groups when waiting in line for food at a fast food counter. The first groupbought 7 slices of pizza and 4 soft drinks for $31.35. The second group bought 5 slices of pizza and 5 softdrinks for $26.40. How much does one slice of pizza cost?

Solve the system of equations by elimination. -

Write the word or phrase that best completes each statement or answers the question. -The perimeter of a parking lot is 500 yards. Find the dimensions of the lot if the length is 50 yards morethan three times the width.

Solve the system of equations. [Hint: Let , and solve for u and v. Then let -

Solve the system of equations by elimination. -

Solve the system of equations by elimination. -

Solve the problem. -A flat rectangular piece of aluminum has a perimeter of 58 inches. The length is 7 inches longer than thewidth. Find the width.

Solve the system of equations by elimination. -

Solve the system of equations by elimination. -

Solve the problem. -The Family Fine Arts Center charges $22 per adult and $14 per senior citizen for its performances. On arecent weekend evening when 571 people paid admission, the total receipts were $9,378. How many whopaid were senior citizens?

Solve the problem. -A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and thetheater collected $272.00 at the end of the day, how many of them were adults?

Solve the problem. -A retired couple has $180,000 to invest to obtain annual income. They want some of it invested in safeCertificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 11% per year. Howmuch should they invest in each to realize exactly $17,300 per year?

Solve the system of equations by elimination. -