Chapter 8 Systems Of Linear Equations And Inequalities Worksheet With Answers Page 9
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Chapter 8 Systems of Linear Equations and Inequalities
37. x
y
4
38. y
2x
3
$824 and twice as many adult tickets as student tickets
were sold, then how many of each were sold?
x
y
5
y
3x
3
53. Corporate taxes. According to Bruce Harrell, CPA, the
amount of federal income tax for a class C corporation
39. 2x
y
4
40. y
3(x
4)
is deductible on the Louisiana state tax return, and the
2x
y
3
3x
y
12
amount of state income tax for a class C corporation is
deductible on the federal tax return. So for a state tax
rate of 5% and a federal tax rate of 30%, we have
41. 3(y
1)
2(x
3)
42. y
3x
3y
2x
3
y
3x
1
state tax
0.05(taxable income
federal tax)
and
43. x
y
0.375
44. y
2x
1.875
federal tax
0.30(taxable income
state tax).
1.5x
3y
2.25
2.5y
3.5x
11.8125
Find the amounts of state and federal income tax for a
class C corporation that has a taxable income of
$100,000.
In Exercises 45–58, write a system of two equations in two
54. More taxes. Use information given in Exercise 53 to
unknowns for each problem. Solve each system by substitu-
find the amounts of state and federal income tax for a
tion. See Examples 7 and 8.
class C corporation that has a taxable income of
45. Perimeter of a rectangle. The length of a rectangular
$300,000. Use a state tax rate of 6% and a federal tax
swimming pool is 15 feet longer than the width. If the
rate of 40%.
perimeter is 82 feet, then what are the length and width?
55. Cost accounting. The problems presented in this exer-
cise and the next are encountered in cost accounting. A
46. Household income. Alkena and Hsu together earn
company has agreed to distribute 20% of its net income
$84,326 per year. If Alkena earns $12,468 more per year
N to its employees as a bonus; B
0.20N. If the com-
than Hsu, then how much does each of them earn per
pany has income of $120,000 before the bonus, the
year?
bonus B is deducted from the $120,000 as an expense to
determine net income; N
120,000
B. Solve the
system of two equations in N and B to find the amount
47. Different interest rates. Mrs. Brighton invested
of the bonus.
$30,000 and received a total of $2,300 in interest. If she
invested part of the money at 10% and the remainder at
56. Bonus and taxes. A company has an income of
5%, then how much did she invest at each rate?
$100,000 before paying taxes and a bonus. The bonus B
is to be 20% of the income after deducting income taxes
T but before deducting the bonus. So
48. Different growth rates. The combined population of
Marysville and Springfield was 25,000 in 1990. By 1995
B
0.20(100,000
T ).
the population of Marysville had increased by 10%,
while Springfield had increased by 9%. If the total popu-
Because the bonus is a deductible expense, the amount
lation increased by 2380 people, then what was the popu-
of income tax T at a 40% rate is 40% of the income after
lation of each city in 1990?
deducting the bonus. So
T
0.40(100,000
B).
49. Finding numbers. The sum of two numbers is 2, and
their difference is 26. Find the numbers.
50. Finding more numbers. The sum of two numbers is
100
16, and their difference is 8. Find the numbers.
T
0.40(100,000
B)
80
51. Toasters and vacations. During one week a land devel-
60
oper gave away Florida vacation coupons or toasters to
B
0.20(100,000
T)
100 potential customers who listened to a sales presenta-
40
tion. It costs the developer $6 for a toaster and $24 for a
20
Florida vacation coupon. If his bill for prizes that week
was $708, then how many of each prize did he give
0
0
20
40
60
80 100
away?
Taxes (in thousands of dollars)
52. Ticket sales. Tickets for a concert were sold to adults
for $3 and to students for $2. If the total receipts were
F I G U R E F O R E X E R C I S E 5 6
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