Four numbers have a sum of 9900. the second exceeds the first by 1/7 of the first. the third exceeds the sum of the first two by 300. the fourth exceeds the sum of the first three by 300. find the four numbers.

Numbers are 1050, 1200, 2550, 5100.

Step-by-step explanation:

Let the four numbers are a, b, c, d.

Since second exceeds the first by 1/7 of the first.

b = a + (a/7) = 8a/7

Third exceeds the sum of first two by 200.

c = a + b + 300 = a + (8a/7) + 300 = (15a/7) + 300

Fourth exceeds the sum of the first three by 300

d = a + b + c + 300 = a + (8a/7) + (15a/7) + 300 + 300 = a + (23a/7) + 600

d = (30a/7)+600

And sum of four numbers is 9900

a + b + c + d = 9900(1)

By putting the values of b, c, d in the equation (1)

a + (8a/7) + (15a/7) + 300 + (30a/7) + 600 = 9900

a + (8a/7) + (15a/7) + (30a/7) = 9900 - 300 - 600 = 9000

a + [(8a + 15a + 30a)/7] = 9000

a + (53a/7) = 9000

60a/7 = 9000

a = 9000×7/60 = 1050

Now we put the values of a and get the numbers

b = 8a/7 = 8×1050/7 = 8×150 = 1200

c = (15a/7) + 300 = (15×1050)/7 + 300 = 15×150 + 300 = 2250 + 300 = 2550

and finally from equation 1

1050 + 1200 + 2550 + d = 9900

d + 4800 = 9900

d = 9900 - 4800 = 5100

Therefore the numbers are 1050, 1200, 2550 & 5100.

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation:

5+2x=a

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