28% of Sumiko's CDs are Chinese music CDs. 42% of these are English music CDs and the rest are Japanese music CDs. There are 45 Japanese music CDs. Find the total number of CDs.

150 CDs

Step-by-step explanation:

From the question, we are told that:

28% of Sumiko's CDs are Chinese music CDs.

42% of these are English music CDs The rest are Japanese music CDs.

Let the total number of CDs = 100%

Therefore the percentage of Japanese CDs is calculated as:

100% - (28% + 42%)

100% - 70%

= 30%

There are 45 Japanese music CDs.

Let us represent total number of CDs = x

Hence,

30% of x = 45 Japanese music CDs

Hence,

30/100 × x = 45

30x/100 = 45

Cross Multiplication

30x = 100 × 45

Divide both sides by 30

x = 4500/30

x = 150 CDs

Therefore, the total number of CDs = 150 CDs

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

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