SOLVE THE EQUATION BY FIRST CLEARING THE DECIMALS

Problem 2 :

7.8y + 6 = 23.16

Solution :

Subtract 6 from both sides

7.8y + 6 - 6 = 23.16 – 6

7.8y = 17.16

Divide both sides by 7.8

7.8y / 7.8= 17.16 / 7.8

y = 2.2

Problem 3 :

10.7w + 4 = 47.87

Solution :

Subtract 4 from both sides

10.7w + 4 - 4 = 47.87 – 4

10.7w = 43.87

Divide both sides by 10.7

10.7w / 10.7 = 43.87 / 10.7

w = 4.1

Problem 4 :

2 = -6.4z + 10

Solution :

By Swap,

-6.4z + 10 = 2

Subtract 10 from both sides

-6.4z + 10 – 10 = 2 – 10

-6.4z = -8

Divide both sides by -6.4

-6.4z / -6.4= -8 / -6.4

z = 1.25

Problem 5 :

-3.3x + 6.5 = 1.55

Solution :

Subtract 6.5 from both sides

-3.3x + 6.5 – 6.5 = 1.55 – 6.5

-3.3x = -4.95

Divide both sides by -3.3

-3.3x / -3.3 = -4.95 / -3.3

x = 1.5

Problem 6 :

1.6b – 3 = -9.4

Solution :

Add 3 to both sides

1.6b – 3 + 3 = -9.4 + 3

1.6b = -6.4

Divide both sides by 1.6

1.6b / 1.6 = -6.4 / 1.6

b = -4

Problem 7 :

-1.7w – 4 = 2.63

Solution :

Add 4 to both sides

-1.7w – 4 + 4 = 2.63 + 4

-1.7w = 6.63

Divide both sides by -1.7

-1.7w / -1.7 = 6.63 / -1.7

w = -3.9

Problem 8 :

2.875y + 9 = 12.45

Solution:

Subtract 9 from both sides

2.875y + 9 - 9 = 12.45 – 9

2.875y = 3.45

Divide both sides by 2.875

2.875y / 2.875 = 3.45 / 2.875

y = 1.2

Problem 9 :

4.125c + 5 = -9.85

Solution :

Subtract 5 from both sides

4.125c + 5 - 5 = -9.85 – 5

4.125c = -14.85

Divide both sides by 4.125

4.125c / 4.125 = -14.85 / 4.125

c = -3.6

Problem 10 :

Your parents give you $20 to help buy the new pair of shoes shown. After you buy the shoes, you have $5.50 left. Write and solve an equation to find how much money you had before your parents gave you $20.

Solution :

Cost of pair of shoes = $59

Your parents giving you = $20

Amount you have left = $5.50

Let x be the amount you have previously.

x + 20 + 5.50 = 59

x + 25.50 = 59

x = 59 - 25.50

x = $33.50

So, your parents should give you $33.50.

Problem 11 :

You participate in a dance-a-thon fundraiser. After your parents pledge $15.50 and your neighbor pledges $8.75, you have $66.55. Write and solve an equation to find how much money you had before your parents and neighbor pledged.

Solution :

The amount i have = $66.55

Amount your parents pledges = $15.50

Amount your neighbor pleges = $8.75

Let x be the amount you have before they pledge.

x + 15.50 + 8.75 = 66.55

x + 24.25 = 66.55

x = 66.55 - 24.25

x = 42.3

So, the amount you have before they pledge is $42.3.

Problem 12 :

You have $15.

a. How much money do you have left if you ride each ride once?

b. Do you have enough money to ride each ride twice? Explain.

Solution :

Cost for Bumber car = $1.75

Cost for Gaint slide = 1.75 - 0.50

= 1.25

Cost for Ferris wheel = 1.50 + 0.50

= 2

Cost for Roller coaster = 1.25 + 2

= 3.25

When you ride once, the amount spent for it = 1.75 + 1.25 + 2 + 3.25

= 8.25

a) After the amount spent for ride = 15 - 8.25

= 6.75

b) amount should be spent when we ride twice = 2(8.25)

= $16

Since you have $15, the amount will not be enough.

Problem 13 :

In the 2012 Olympics, Usain Bolt won the 200-meter dash with a time of 19.32 seconds. Write and solve an equation to find his average speed to the nearest hundredth of a meter per second.

Solution :

d = r ⋅ t

200 = r ⋅ 19.32

r = 200/19.32

r = 10.35 seconds

Problem 14 :

A discounted amusement park ticket costs $12.95 less than the original price p. Write and solve an equation to find the original price.

Solution :

Original price is p

p - 12.95 = discounted price

p - 12.95 = 44

p = 44 + 12.95

p = 56.95

So, the original price is $59.95.