QNT 501 Final EXAM 7
1. Solve for the unknown in the equation. 11A = 77
Divide both sides of the equation by the known factor to isolate the unknown value. 11 A 11 = 77 11 Now
simplify. A= 7 Check. 11(7) = 77 77 = 77 Therefore, the solution of the equation is 7.
2. Solve for the unknown in the equation. B + 5 = 21
Subtract the known value from both sides of the equation to isolate the unknown value. B + 5 (5) = 21 (5)
Now simplify. B = 16 Check. 16 + 5 = 21 21 = 21 Therefore, the solution of the equation is 16.
3. Solve for the unknown in the equation. X 53 = 27
Add the known value to both sides of the equation. X 53 + (53) = 27 + (53) Now simplify. X = 80 Check.
80 53 = 27 27 = 27 Therefore, the solution of the equation is 80.
4. Solve for the unknown in the equation. 5(X - 4) = 25
Eliminate the parentheses. 5X 20 + (20) = 25 + (20) Now simplify. 5X = 45 Divide both sides of the
equation by the known factor to isolate the unknown value. 5X 5 = 45 5 Now simplify. X=9 Check the
solution by substituting the answer in the original equation and verifying that a true statement result. The
answer checks, so the solution of the equation is 9.
5. Many plans to save 1 14 of this salary each week . If his weekly salary is $ 434, find the amount he will
save each week
S= 1 1 ($31) S = $31 To check the solution, replace S with $31 and see if the sides are equal . ¿ $ 31 ¿ ?
¿ 1 ( $ 434 ) 14 ¿ $ 31 ¿ ? ¿ 1 ($ 434) 14 $31= $31 The answer checks Thus, Manny will save $31 each
week.
6. Last week at a festival, a man sold 4 times as many tie dyed T- shirt as silk screened shirts. He sold
225 shirts altogether. How many tie-dyed shirts did he sell?
Both the number of tie-dyed T-shirts and silk screened shirts are unknown, but choose one, silk-screened
shirts, to be represented by a letter, N. Since the number of tie-dyed shirts is 4 times the number silk-
screened shirts, represent the number of tie-dyed T-shirts as 4N. Tie-dyed shirts plus silk screened shirts
equals total shirts. Write this information in symbols. N + 4N = 225 Solve the equation. Combine addends.
N + 4N = 225 5N = 225 Divide both sides by 5. 5N 5 = 225 5 N = 45 The solution is 45, which represents
the number of silk-screened shirts, check the solution by replacing N with 45. 45 + 4(45) = 225 45 + 180 =
225 225 = 225 The sides are equal. Therefore, the number of silk-screened shirts is 45 and the number of
tie-dyed shirts is 180
7. A man ordered 3 times as many boxes of ballpoint pens as boxes of felt-tip pens. Ballpoint pens cost
$4.14 per box, and felt-tip pens cost $3.05. If the mans order of pens totaled $77.35, how many boxes of
each type of pen did he buy?
15.47 N 15.47 = 77.35 15.47 N=5 The solution is 5, which represent the number of boxes of felt tip pens.
Check the solution by replacing N with 5. 3.05(5) + (4.14 * 3(5) ) = 77.35 3.05(5) + 12.42(5) = 77.35 15.25
+ 62.10 = 77.35 77.35 = 77.35 The sides are equal. Therefore, the man ordered 5 boxes of felt-tip pens
and 15 boxes of ballpoint pens.
, 8. For 28 hours of work, you are paid $208.60. How much would you receive for 36 hours? Set up an
equation for the problem.
The amount of money received for 28 hours of work is proportional to the amount of money received for
36 hours of work. $ 208.60 28 hour D dollars 36 hour = Solve the equation. 208.60 28 D 36 = 28 D =
(208.60 * 36) Cross multiply. 28 D = 7,509.60 Multiply. Divide both sides by 28. 28D = 7,509.60 28 D 28
7,509.60 28 = D = 268.20 To check the solution, replace D with 268.20 and see if the sides are equal.
208.60 28 7.45 = 7.45 ¿ ? ¿ ¿ D 36 Divide. The solution checks . Therefore, you would receive $268.20
for 36 hours of work.
9. NA
10. Two part-time employees share one full time job. A girl works Mondays, Wednesdays, and Fridays,
and a boy works Tuesdays and Thursdays. The job pays an annual salary of $28,632. What annual salary
does each employee earn?
Many businesses related problems that involve pairs of numbers that are proportional are direct
proportions. That an increases in the number that pairs with it..Or, a decrease in one amount causes a
decrease in the second amount. In the given problem, the job pays an annual salary of $28,632. Two
employees work 5 days. Let s equal the amount of the girls salary. The amount of the annual salary,
$2,632, per 5 days in proportional to the amount of the girls salary per 3 day.. Set up a proportion. 5 3 = $
28,632 S Solve the proportion. Cross multiply. 5 S = 3 (28,632) = 85,896 Divide both sides by 5. 5S 5 =
85,896 5 S = 17,179.20 To determine the amount of the boys salary, subtract $17,179.20 from $28,632.
$28,632 - $17,179.20 = $11,452.80 Therefore, the girls salary is $17, 79.20 and the boys salary is
$11,452.80.
11. The formula Total cost = Cost + Shipping cost + Installation is used to find the total cost of a business
asset. The formula can be written in symbols as T = C + S + I. Solve the formula for S, the shipping cost
of the asset.
To solve the formula for S, find an equivalent formula by rearranging it. Treat all the variables of the
formula as numbers in equation. To isolate S on the right side, choose one of the terms, C or I, to subtract
from both sides of the equation. First, subtract C from both sides of the equation and simplify. T=C+S+I
TC=C+S+IC Subtract C from both sides of the equation. TC=S+I Next, subtract I from both sides of the
equation and simplify. TC=S+I TC-I=C+S+II Subtract I from both sides of the equation. TCI=S Finally,
interchange the sides of the equation. S=TCI Thus, Shipping cost = Total cost Cost Installation.
12. The formula, Salvage value = total cost depreciable Value, is used to set up a depreciation schedule
for an asset. The formula can be written in symbols as S = C V. Solve the formula for C.
To solve the formula for C, find an equivalent formula by rearranging it. Treat all the variables of the
formula as numbers in an equation. To isolate C on the right side, add V to both sides of the equation.
Solve for C. S=CV S+V=CV+V Add V to both sides of the equation. S+V=C Simplify. Finally, interchange
the sides of the equation. C=S+V Therefore, total Cost = Salvage value + depreciable Value.
13. The formula, years of expected Life = depreciable Value Yearly depreciation is used to find yearly
depreciation using the line depreciation method. The formula can be written in symbols as L = V Y . Solve
the formula for V.
To solve the formula for V , find an equivalent formula by rearranging it. Treat all the variable of the
formula as number in an equation. To isolate V on the right side, multiply both sides of equation by Y .
1. Solve for the unknown in the equation. 11A = 77
Divide both sides of the equation by the known factor to isolate the unknown value. 11 A 11 = 77 11 Now
simplify. A= 7 Check. 11(7) = 77 77 = 77 Therefore, the solution of the equation is 7.
2. Solve for the unknown in the equation. B + 5 = 21
Subtract the known value from both sides of the equation to isolate the unknown value. B + 5 (5) = 21 (5)
Now simplify. B = 16 Check. 16 + 5 = 21 21 = 21 Therefore, the solution of the equation is 16.
3. Solve for the unknown in the equation. X 53 = 27
Add the known value to both sides of the equation. X 53 + (53) = 27 + (53) Now simplify. X = 80 Check.
80 53 = 27 27 = 27 Therefore, the solution of the equation is 80.
4. Solve for the unknown in the equation. 5(X - 4) = 25
Eliminate the parentheses. 5X 20 + (20) = 25 + (20) Now simplify. 5X = 45 Divide both sides of the
equation by the known factor to isolate the unknown value. 5X 5 = 45 5 Now simplify. X=9 Check the
solution by substituting the answer in the original equation and verifying that a true statement result. The
answer checks, so the solution of the equation is 9.
5. Many plans to save 1 14 of this salary each week . If his weekly salary is $ 434, find the amount he will
save each week
S= 1 1 ($31) S = $31 To check the solution, replace S with $31 and see if the sides are equal . ¿ $ 31 ¿ ?
¿ 1 ( $ 434 ) 14 ¿ $ 31 ¿ ? ¿ 1 ($ 434) 14 $31= $31 The answer checks Thus, Manny will save $31 each
week.
6. Last week at a festival, a man sold 4 times as many tie dyed T- shirt as silk screened shirts. He sold
225 shirts altogether. How many tie-dyed shirts did he sell?
Both the number of tie-dyed T-shirts and silk screened shirts are unknown, but choose one, silk-screened
shirts, to be represented by a letter, N. Since the number of tie-dyed shirts is 4 times the number silk-
screened shirts, represent the number of tie-dyed T-shirts as 4N. Tie-dyed shirts plus silk screened shirts
equals total shirts. Write this information in symbols. N + 4N = 225 Solve the equation. Combine addends.
N + 4N = 225 5N = 225 Divide both sides by 5. 5N 5 = 225 5 N = 45 The solution is 45, which represents
the number of silk-screened shirts, check the solution by replacing N with 45. 45 + 4(45) = 225 45 + 180 =
225 225 = 225 The sides are equal. Therefore, the number of silk-screened shirts is 45 and the number of
tie-dyed shirts is 180
7. A man ordered 3 times as many boxes of ballpoint pens as boxes of felt-tip pens. Ballpoint pens cost
$4.14 per box, and felt-tip pens cost $3.05. If the mans order of pens totaled $77.35, how many boxes of
each type of pen did he buy?
15.47 N 15.47 = 77.35 15.47 N=5 The solution is 5, which represent the number of boxes of felt tip pens.
Check the solution by replacing N with 5. 3.05(5) + (4.14 * 3(5) ) = 77.35 3.05(5) + 12.42(5) = 77.35 15.25
+ 62.10 = 77.35 77.35 = 77.35 The sides are equal. Therefore, the man ordered 5 boxes of felt-tip pens
and 15 boxes of ballpoint pens.
, 8. For 28 hours of work, you are paid $208.60. How much would you receive for 36 hours? Set up an
equation for the problem.
The amount of money received for 28 hours of work is proportional to the amount of money received for
36 hours of work. $ 208.60 28 hour D dollars 36 hour = Solve the equation. 208.60 28 D 36 = 28 D =
(208.60 * 36) Cross multiply. 28 D = 7,509.60 Multiply. Divide both sides by 28. 28D = 7,509.60 28 D 28
7,509.60 28 = D = 268.20 To check the solution, replace D with 268.20 and see if the sides are equal.
208.60 28 7.45 = 7.45 ¿ ? ¿ ¿ D 36 Divide. The solution checks . Therefore, you would receive $268.20
for 36 hours of work.
9. NA
10. Two part-time employees share one full time job. A girl works Mondays, Wednesdays, and Fridays,
and a boy works Tuesdays and Thursdays. The job pays an annual salary of $28,632. What annual salary
does each employee earn?
Many businesses related problems that involve pairs of numbers that are proportional are direct
proportions. That an increases in the number that pairs with it..Or, a decrease in one amount causes a
decrease in the second amount. In the given problem, the job pays an annual salary of $28,632. Two
employees work 5 days. Let s equal the amount of the girls salary. The amount of the annual salary,
$2,632, per 5 days in proportional to the amount of the girls salary per 3 day.. Set up a proportion. 5 3 = $
28,632 S Solve the proportion. Cross multiply. 5 S = 3 (28,632) = 85,896 Divide both sides by 5. 5S 5 =
85,896 5 S = 17,179.20 To determine the amount of the boys salary, subtract $17,179.20 from $28,632.
$28,632 - $17,179.20 = $11,452.80 Therefore, the girls salary is $17, 79.20 and the boys salary is
$11,452.80.
11. The formula Total cost = Cost + Shipping cost + Installation is used to find the total cost of a business
asset. The formula can be written in symbols as T = C + S + I. Solve the formula for S, the shipping cost
of the asset.
To solve the formula for S, find an equivalent formula by rearranging it. Treat all the variables of the
formula as numbers in equation. To isolate S on the right side, choose one of the terms, C or I, to subtract
from both sides of the equation. First, subtract C from both sides of the equation and simplify. T=C+S+I
TC=C+S+IC Subtract C from both sides of the equation. TC=S+I Next, subtract I from both sides of the
equation and simplify. TC=S+I TC-I=C+S+II Subtract I from both sides of the equation. TCI=S Finally,
interchange the sides of the equation. S=TCI Thus, Shipping cost = Total cost Cost Installation.
12. The formula, Salvage value = total cost depreciable Value, is used to set up a depreciation schedule
for an asset. The formula can be written in symbols as S = C V. Solve the formula for C.
To solve the formula for C, find an equivalent formula by rearranging it. Treat all the variables of the
formula as numbers in an equation. To isolate C on the right side, add V to both sides of the equation.
Solve for C. S=CV S+V=CV+V Add V to both sides of the equation. S+V=C Simplify. Finally, interchange
the sides of the equation. C=S+V Therefore, total Cost = Salvage value + depreciable Value.
13. The formula, years of expected Life = depreciable Value Yearly depreciation is used to find yearly
depreciation using the line depreciation method. The formula can be written in symbols as L = V Y . Solve
the formula for V.
To solve the formula for V , find an equivalent formula by rearranging it. Treat all the variable of the
formula as number in an equation. To isolate V on the right side, multiply both sides of equation by Y .
