Multi-Step Equations
Solve for m:
5 = 5m - 23 + 2m
m =4
WORK
5 = 5m - 23 + 2m
5 = 5m + 2m - 23
5 = 7m - 23
5 + 23 = 7m - 23 + 23
28 = 7m
28/7 = 7m/7
4 = m
Solve for b:
3b - 4 = b + 2
b = 3
WORK
3b - 4 = b + 2
3b - 4 + 4 = b + 2 + 4
3b = b + 6
3b - b = b - b + 6
2b = 6
2b/2 = 6/2
b = 3
Solve for z:
3/4 = z/16
z = 12
WORK
4z = 3(16)
4z = 48
4z/4 = 48/4
z = 12
Solve:
42 is 40% of what number?
105
WORK
40/100 = 42/x
40x = 42(100)
40x = 4200
40x/40 = 4200/40
x = 105
Solve:
Five friends equally split a restaurant bill that comes to $32.50. How much does each friend pay?
Each friend pays $6.50.
WORK
5x = 32.50
5x/5 = 32.50/5
x = 6.5 ~~~> $6.50
Solve for x:
(x + 4) + 2x = 67
x = 21
WORK
(x + 4) + 2x = 67
x + 2x + 4 = 67 [addition is commutative]
3x + 4 = 67
3x + 4 - 4= 67 - 4
3x = 63
3x/3 = 63/3
x = 21
Solve for x:
5x + 2 = 2x + 14
x = 4
WORK
5x + 2 = 2x + 14
5x + 2 - 2 2x + 14- 2
5x = 2x + 12
5x - 2x = 2x - 2x + 12
3x = 12
3x/3 = 12/3
x = 4
Solve for k:
k/9 = 63/81
k = 7
WORK
81k = 9(63)
81k = 567
81k/81 = 567/81
k = 7
Solve:
117 is 78% of what number?
150
WORK
78/100 = 117/x
78x = 117(100)
78x = 11700
78x/78 = 11700/78
x = 150
Solve:
You work for 4 hours on Saturday and 8 hours on Sunday. You receive a $50 bonus. You earn $164.00 total. How much did you earn per hour?
You earned $9.50 per hour.
WORK
4x + 8x + 50 = 164
12x + 50 = 164
12x + 50 - 50 = 164 - 50
12x = 114
12x/12 = 114/12
x = 9.5 ~~~> $9.50
Solve for x:
-8(2x - 1) = 36
x = -7/4
WORK
-8(2x - 1) = 36
-16x + 8 = 36 [Distributive Property]
-16x + 8 - 8 = 36 - 8
-16x = 28
-16x/(-16) = 28/(-16)
x = -7/4
Solve for p:
1.5p = 1.25p + 8
p = 32
WORK
1.5p = 1.25p + 8
1.5p - 1.25p = 1.25p - 1/25p + 8
0.25p/0.25 = 8/0.25
p = 32
Solve for n:
-5n/4 = 15/2
n = -6
WORK
-5n(2) = 15(4)
-10n = 60
-10n/-10 = 60/-10
n = -6
Solve:
What percent of 124 is 93?
75%
WORK
x/100 = 93/124
124x = 93(100)
124x = 9300
124x/124 = 9300/124
x = 75%
Solve:
Two buildings have the same total height. One building has 8 floors with height, h. The other building has a ground floor of 16ft and 6 other floors with height, h. Write and solve an equation to find the height, h, of these floors.
8h = 16 + 6h
h = 8
WORK
8h = 16 + 6h
8h - 6h = 16 + 6h - 6h
2h = 16
2h/2 = 16/2
h = 8
Solve for x:
3.5 - 0.02x = 1.24
x = 113
WORK
3.5 - 0.02x = 1.24
100*(3.5 - 0.02x) = 1.24*100
350 - 2x = 124 [Distributive Property]
350 - 350 - 2x = 124 - 350
-2x/(-2) = -226/(-2)
x = 113
Solve for x:
2(5x - 1) = 3(x + 11)
x = 5
WORK
2(5x - 1) = 3(x + 11)
10x - 2 = 3x + 33 [Distribute]
10x - 3x - 2 = 3x - 3x + 33
7x - 2 + 2 = 33 + 2
7x/7 = 35/7
x = 5
Solve for x:
34/6 = (2x+1)/3
x = 8
WORK
6(2x+1) = 34(3)
12x + 6 = 102
12x + 6 - 6 = 102 - 6
12x = 96
12x/12 = 96/12
x = 8
Solve:
What number is 44% of 24.5?
10.78
WORK
44/100 = x/24.5
100x = 24.5(44)
100x = 1078
x = 10.78
Solve
Online concert tickets cost $37 each, plus a service charge of $8.50 per ticket. The Web site also charges a transaction fee of $14.99 for the purchase. You paid $242.49. How many tickets did you buy?
You bought 5 tickets.
WORK
37t + 8.50t + 14.99 = 242.49
45.5t + 14.99 = 242.49
45.5t + 14.99 - 14.99 = 242.49 - 14.99
45.5t = 227.5
45.5t/45.5 = 227.5/45.5
t = 5 ~~~> 5 tickets
Solve for x:
3x/4 - x/3 = 10
x = 24
WORK
3x/4 - x/3 = 10
9x/12 - 4x/12 = 10 [write fractions/common denominator]
5x/12 = 10
12*(5x/12) = 10*12
5x/5 = 120/5
x = 24
Solve for x:
9m - 4 = -3m + 5 + 12m
NO SOLUTION
-4 = 5
WORK
9m - 4 = -3m + 5 + 12m
9m - 4 = -3m + 12m + 5
9m -9m - 4 = 9m -9m + 5
-4 = 5 <~~~NO! So, No Solution!
Solve for a:
(-4a - 1)/(-10a) = 3/8
a = -4
WORK
8(-4a - 1) = 3(-10a)
-32a - 8 = -30a
-32a - 8 + 32a = -30a + 32a
-8 = 2a
-8/2 = 2a/2
a =-4
Solve:
79.8 is what percent of 95?
84%
WORK
x/100 = 79.8/95
95x = 79.8(100)
95x = 7980
95x/95 = 7980/95
x = 84%
Solve
Pristine Printing will print business cards for $0.10 each plus a setup charge of $15. The Printing Place offers business cards for $0.15 each with a setup charge of $10. What number of business cards costs the same from either printer? BONUS: What would the cost be?
Printing 100 cards would cost the same from either business.
WORK
0.10n + 15 = 0.15n + 10
0.10n - 0.10n + 15 = 0.15n - 0.10n +10
15 = 0.05n + 10
15 - 10 = 0.05n + 10 - 10
5 = 0.05n
5/0.05 = 0.05n/0.05
100 = n ~~~>100 cards
BONUS answer: It would cost $25.00 to make 100 cards from either place.
WORK
0.10n + 15 = ??
0.10(100) + 15 = 25 ~~~>$25.00
0.15n + 10 = ??
0.15(100) + 10 = 25 ~~~>$25.00