Explanation:
wow ! you really don't know how to do even the simplest ones ? then you should ask your teacher for help too.
or you are just too lazy to do your homework ?
1.
6n = 42 / divide both sides by 6
6n/6 = 42/6
n = 7
2.
3y = 192 / divide both sides by 3
3y/3 = 192/3
y = 64
3.
8x = 72 / divide both sides by 8
8x/8 = 72/8
x = 9
4.
4 = 2a / divide both sides by 2
4/2 = 2a/2
2 = a
or
a = 2 / that is the beauty of an equation
as both sides are equal, we can
write them in any sequence.
5.
7n = 112 / well ? divide both sides by 7
7n/7 = 112/7
n = 16
6.
84 = n - 19 / add 19 to both sides
84 + 19 = n - 19 + 19
103 = n
or
n = 103
Mike has 103 cards.
7.
Jamie = 3 × Michelle
Jamie = 12 mph
we use this in the first equation :
12 = 3 × Michelle / divide both sides by 3
12/3 = 3 × Michelle / 3
4 = Michelle
Michelle can jog at 4 mph.
8.
5 + r = 6 - r / add r to both sides
5 + r + r = 6 - r + r
5 + 2r = 6 / subtract 5 from both sides
5 + 2r - 5 = 6 - 5
2r = 1 / divide both sides by 2
2r/2 = 1/2
r = 1/2
9.
z - 16 = -16 / add 16 to both sides
z - 16 + 16 = -16 + 16
z = 0
10.
7n - 7 = 0 / add 7 to both sides
7n - 7 + 7 = 0 + 7
7n = 7 / divide both sides by 7
7n/7 = 7/7
n = 1
11.
15 m/s is the speed (which is always distance per duration).
we need to go 1350 m.
so, we need as many seconds as how many times 15 fits into 1350 :
1350 / 15 = 90
it will take the boat 90 seconds to cross the river. that is 1.5 minutes (remember, 60 seconds = 1 minute).
12.
the speed is 55 miles/hour.
they want to travel 440 miles.
it will take them as many hours as how many times 55 fits into 440 :
440 / 55 = 8
it will take them 8 hours.
13.
the speed is 8 m/s.
now we want to know how far he can swim in 1.5 minutes.
remember, 60 seconds = 1 minute.
1.5 minutes = 60 + 60/2 = 60 + 30 = 90 seconds.
8 meters in 1 second. how many meters in 90 seconds ?
well,
8×90 = 720 meters.
the swimmer can swim 720 meters in 1.5 minutes.
14.
the speed is 650 miles/hour.
that means 650 miles in 1 hour.
so, far can it travel in 2 hours ?
650 × 2 = 1300 miles
it can travel 1300 miles in 2 hours.
15.
q = number of quarters (each worth $0.25)
d = number of dimes (each worth $0.10)
q + d = 5
q = 5 - d
0.25q + 0.1d = 1.95
now we use the first equation (identity) in the second :
0.25(5 - d) + 0.1d = 1.95
1.25 - 0.25d + 0.1d = 1.95
-0.15d = 0.7
d = 0.7/-0.15 = -4.666666666...
huh ! a negative number of coins. that tells us this has no solution. it cannot work. 5 such coins can never have the total value of $1.95. as the maximum is 5×0.25 = $1.25.
16.
the speed is 125 km/h.
that means 125 km in 1 hour.
how far in 3 hours ?
125 × 3 = 375 km
it can travel 375 km in 3 hours.
17.
he went 2 + 3 = 5 blocks west.
5 blocks east.
7 blocks north.
4 blocks south.
so, in total, he went 7-4 = 3 blocks north, and 5-5 = 0 blocks east/west.
so, he was 3 blocks away from his home.
18.
he still needs
450 - 296.55 = $153.45
19.
e.g. 2 weeks of work have 10 workdays.
one work week has therefore 10/2 = 5 workdays.
20.
x/4 = 9 / multiply both sides by 4
4×x/4 = 9×4
x = 36
21.
a/5 = 7 / multiply both sides by 5
5×a/5 = 7×5
a = 35
22.
n/3 = 29 / multiply both sides by 3
3×n/3 = 29×3
n = 87
23.
n/3 = 10 / multiply both sides by 3
3×n/3 = 10×3
n = 30
24.
y/5 = 24 / multiply both sides by 5
5×y/5 = 24×5
y = 120
25.
n/8 = 2.5 / multiply both sides by 8
8×n/8 = 2.5×8
n = 20
26.
n + 6.05 = 12.4 / subtract 6.05 from both sides
n + 6.05 - 6.05 = 12.4 - 6.05
n = 6.35
27.
s = Stacy's age
m = her mother's age
m = 36
s = m/4
s = 36/4 = 9
Stacy is 9 years old.
28.
x = time to do the whole job
x/3 = 24 / multiply both sides by 3
3x/3 = 24×3
x = 72 hours
it takes 72 hours to finish the whole job.