CHAPTER 4 | ALGEBRA
EXERCISE 4.3
Answers to the odd numbered problems are available online
1.
Bob earns twice as much per week as Ray. Bob earns $550. How much does Ray earn?
2.
A store sold a total of 150 plasma and LCD model TVs last week. If two times as many plasma
models were sold compared to LCD models, how many of each were sold?
3.
Henry’s pays a monthly flat rate of $25 for his phone and an additional $0.50 per minute for
phone use. If his bill this month was $50, how many minutes did he use?
4.
A salesman receives a base salary of $2,000 a month and an additional $100 for each computer
he sells. How many computers did he sell this month if his salary was $3,000?
5.
In a class of 18 students, there were 4 more girls than boys. How many boys were there in the
class?
6.
Of 46 applicants for a job, there were 18 more graduates than non-graduates. How many graduates
applied for the job?
7.
James works 2.5 hours longer than Perry every week. If James works 36 hours every week, how
long does Perry work?
8.
Andrew’s daily shift is 2 hours shorter than Eva’s. If Andrew worked 6.5 hours yesterday, how
long did Eva work?
9.
$1,000 is shared between Sue and William. Sue’s share is $200 less than William’s. Calculate the
sizes of their shares.
10. $5,000 is shared between Devon and Abby. Devon’s share is $2,000 more than Abby’s share.
Calculate the sizes of their shares.
4.4
ISOLATING A VARIABLE IN A FORMULA
To isolate any variable in a formula, rearrange the variables as shown in the examples below:
EXAMPLE 4.4A - ISOLATING A VARIABLE IN A FORMULA
Isolate ‘h’ in the equation
SOLUTION
A=
(a + b)h
2
(a + b)h
=A
2
(a + b)h
×2 = A×2
2
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(a + b)h
2
Reverse the sides of the equation
Multiply each side by 2
4.4 ISOLATING A VARIABLE IN A FORMULA
(a + b)h = 2 A
Divide each side by (a + b)
(a + b)h
2A
=
(a + b) (a + b)
h=
2A
(a + b)
EXAMPLE 4.4B - SOLVING FOR A VARIABLE IN A FORMULA
P 10
=
, a 2, and c = 6
Find the value of ‘b’ in the equation P = a + b + c if=
SOLUTION
First, isolate the variable ‘b’:
P = a +b+c
Reverse the sides of the equation
a +b+c = P
Subtract ‘a’ from both sides
a −a +b+c = P −a
b+c = P −a
Subtract ‘c’ from both sides
b+c −c = P −a −c
b = P −a −c
Next, substitute the given values and solve for ‘b’:
b = 10 − 2 − 6
b=2
EXERCISE 4.4
Isolate the required variables in Problems 1 and 2.
1.
2.
(a + b)h
2
(c) Isolate ‘M’ in S = C + M
(a) Isolate ‘h’ in A =
(b) Isolate ‘b’ in A = b × h
(d) Isolate ‘B’ in V = B × h
(e) Isolate ‘r’ in I = Prt
(f) Isolate ‘L’ in N = L(1 − d )
(g) Isolate ‘g’ in G = mg
(h) Isolate ‘r’ in S = P (1 + rt )
(i) Isolate ‘x’ in y = mx + b
(j) Isolate ‘t’ in n = m × t
bh
3
(c) Isolate ‘E’ in S = C + E + P
(a) Isolate ‘h’ in V =
j
m
(d) Isolate ‘R’ in P = R × B
(b) Isolate ‘m’ in i =
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CHAPTER 4 | ALGEBRA
3.
4.
5.
(e) Isolate ‘t’ in I = Prt
(f) Isolate ‘m’ in n = m × t
(g) Isolate ‘c’ in V = abc
(h) Isolate ‘P’ in S = P (1 + rt )
(i) Isolate ‘a’ in P = 2a + 2b
(j) Isolate ‘m’ in y = mx + b
Using the formula S = C + E + P , find the values of the required variables:
(a) S = 5.5, C = 2, P = 1, E = ?
(b) S = 17, C = 8, E = 2.5, P = ?
(c) S = 39, E = 6, P = 8, C = ?
(d) C = 12, E = 3, P = 5, S = ?
Using the formula I = Prt , find the values of the required variables:
(a) I = 100, P = 200, t = 10, r = ?
(b) I = 700, P = 2,500, r = 0.04, t = ?
(c) I = 450, r = 0.04, t = 8, P = ?
(d) I =?, P = 3,000, t = 20, r = 0.05
Using the formula P = RB , find the values of the required variables:
(a) B = 400, R = 0.05, P = ?
(b) B = 300, P = 100, R = ?
(c) B = ?, P = 200, R = 0.02
6.
j
, find the values of the required variables:
m
(a) j = 0.12, m = 4, i = ?
Using the formula i =
(b) i = 0.02, m = 2, j = ?
(c) i = 0.03, j = 0.06, m = ?
4.5
4.4
REVIEW
Answers to all the problems are available online
Create algebraic expressions from the mathematical relationships described in Problems 1 and 2:
1.
(a) Three dollars added to the price of two sports’ tickets.
(b) The cost per student of three students sharing the cost of a party.
(c) The selling price of an item if the cost is one-half the selling price.
(d) The price of a text for a sale price of $30 off.
(e) The hourly wage of time and a half.
(f) The cost of five items and then a markup of $15.
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