GIVEN IS WHAT PERCENTAGE OF THE NUMBER

What is percent ?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by whole and multiply by 100.

Hence, the percentage means, a part per hundred. The word per cent means per 100. It represented by the symbol “%”

Problem 1 :

36 is 25% of what number?

Solution :

Let x be the required number.

36 = 25% of x

36 = 0.25 x

Dividing by 0.25 on both sides, we get

36/0.25 = x

x = 144

So, 36 is 25% of 144.

Problem 2 :

8.2% of what number is $2.87?

Solution :

Let x be a number.

8.2% of x = 2.87

0.082 x = 2.87

Divide 0.082 on both sides.

x = 2.87/0.082

x = 35

So, 8.2% of 35 is 2.87.

Problem 3 :

What percent of 1,800 is 846?

Solution :

Let x be a percent.

x% of 1800 = 846

(x/100) ⋅ 1800 = 846

18x = 846

Dividing by 18 on both sides.

x = 846/18

x = 47

So, 47 % of 1800 is 846.

Problem 4 :

What percent of 1,500 is 540?

Solution :

Let x be a percent.

x% of 1500 = 540

(x/100) ⋅ 1500 = 540

15x = 540

Dividing by 15 on both sides.

x = 540/15

x = 36

So, 36% of 1500 is 540.

Problem 5 :

50 is what percent of 40?

Solution :

Let x be a percent.

x% of 40 = 50

(x/100) ⋅ 40 = 50

4x/10 = 50

x = 500/4

x = 125%

So, 50 is 125% of 40.

Problem 6 :

What percent of 260 is 78?

Solution :

Let x be a percent.

x% of 260 = 78

(x/100) ⋅ 260 = 78

26x/10 = 78

26x = 780

Dividing by 26 on both sides.

x = 780/26

x = 30

So, 30% of 260 is 78

Problem 7 :

790 is what percent of 395?

Solution :

Let x be a percent.

x% of 395 = 790

(x/100) ⋅ 395 = 790

395x/100 = 790

Multiplying by 100 on both sides.

395x = 790(100)

Dividing by 395 on both sides.

x = 790(100)/395

x = 200

So, 790 is 200 % of 395.

Problem 8 :

a. Find the percent of sales tax on the food total.

b. Find the amount of a 16% tip on the food total.

Solution :

a. Let x be the sales tax percentage.

Amount spent for food = $27.50

x% of 27.50 = 1.65

(x/100) · 27.50 = 1.65

x = (1.65 · 100)/27.50

x = 165/27.50

x = 6

So, the sales tax is 6%.

b. Amount for tip = 16% of the food total.

= 16% of 27.50

= (16/100) · 27.50

= (16 · 27.50)/100

= $4.4

So, the tip is $4.4.

Problem 9 :

A pitcher throws 75 pitches. Of these, 72% were strikes. How many strikes did the pitcher throw?

Solution :

Total number of pitches = 75

Number of stirkes = 72% of 75

= (72/100) · 75

= (72 · 75)/100

= 54

So, number of strikes the pitcher throw is 54.

Problem 10 :

Your school raised 125% of its fundraising goal. The school raised $6750. What was the goal?

Solution :

The amount raised = 6750

Let x be the amount of fundraising goal.

125% of x = 6750

(125/100) · x = 6750

x = (6750 ·100)/125

x = 5400

So, before raising the original fund was $5400.

Problem 11 :

The sales tax on a surfboard is $12. What is the percent of sales tax?

Cost of surfboard = $240

Sales tax = $12

We should find 12 is what percentage of 240.

Let x be the required percentage.

x% of 240 = 12

(x/100) · 240 = 12

x = (12 · 100)/240

x = 5

So, the sales tax is 5% of sale price.

Problem 12 :

The percents of three types of tickets collected at the gate for a high school football game are shown.

a)  Write the percents as decimal and as fractions.

b) There is one type of ticket that is not shown. It is a ticket for a child under 5. What percent of the tickets were of this type ?

Solution :

a)

Student = 48%

Converting into fraction,

= 48/100 (or) 12/25

Converting into decimal,

= 0.48

Adult = 28%

Converting into fraction,

= 28/100 (or) 7/25

Converting into decimal,

= 0.28

Senior = 14%

Converting into fraction,

= 14/100 (or) 7/50

Converting into decimal,

= 0.14

b)

Total percentage shown = (48 + 28 + 14)%

= 90%

The percentage which is not shown = 100% - 90%

= 10%

So, percentage of ticket for a child under 5 is 10%.

Problem 13 :

There were w signers of the Declaration of Independence. The youngest was Edward Rutledge, who was x years old. The oldest was Benjamin Franklin, who was y years old.

a) x is 25% of 104. What was Rutledge’s age?

b) 7 is 10% of y. What was Franklin’s age?

c) w is 80% of y. How many signers were there?

d) y is what percent of (w + y − x)?

Solution :

a)

x = 25% of 104

= (25/100) · 104

= 26

So, Rutledge is 26 years old.

b)  

7 = 10% of y

7 = (10/100) · y

7 = (1/10) · y

7 = y/10

y = 7(10)

y = 70

c)  

w = 80% of y

w = (80/100) · 70

w = 8 · 7

w = 56

So, number of singers is 56.

d)

y = ?% of (w + y − x)?

Applying the values of the varaibles solved above, we get

70 = ?% (56 + 70 - 26)

70 = ?% (100)

70/100 = ?%

70% = ?%

So, the required percentage is 70%.