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The sum of three numbers is 86. The third number is 4 times the first. The first number is 10 more than the second. What are the numbers?
Question
The sum of three numbers is 86. The third number is 4 times the first. The first number is 10 more than the second. What are the numbers?
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Mathematics
3 years
2021-08-21T15:06:11+00:00
2021-08-21T15:06:11+00:00 1 Answers
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Answer:
The first number is 16
The second number is 6
The third number is 64
Step-by-step explanation:
The information from the word problem are;
The count of the numbers in the sum = 3 numbers
The value of the sum of the three numbers = 86
The value of the third number = 4 × The value of the first number
The value of the first number = 10 + The value of the second
Let ‘x’ represent the first number, let ‘y’ represent the second number and let ‘z’ represent the third number, we have;
x + y + z = 86…(1)
z = 4 × x…(2)
x = y + 10…(3)
From equation (3), we get;
x = y + 10
∴ y = x – 10…(4)
Substituting the value of z from equation (2) and the value of y from equation (4) in equation (1) gives;
x + y + z = 86
z = 4 × x = 4·x
y = x – 10
∴ x + y + z = x + (x – 10) + 4·x = 86
x + (x – 10) + 4·x = x + x – 10 + 4·x = 6·x – 10 = 86
6·x = 86 + 10 = 96
∴ x = 96/6 = 16
x = 16
From equation (2), we get;
z = 4 × x
∴ z = 4 × 16 = 64
z = 64
From equation (4), we get
y = x – 10
∴ y = 16 – 10 = 6
y = 6
Therefore; x = 16, y = 6, and z = 64
The numbers are 16, 6, and 64