Answer:
x = 18 y = 10
Step-by-step explanation:
let the first number be x
let the second number be y
x = y + 8..... equation 1
2x + y = 46.... equation 2
x is the larger number
y is the smaller number.
Rearrange the equation and add equation 1 to equation 2.
x - y = 8
+ 2x + y = 46
-------------------
3x + 0 = 54
3x = 54
divide both sides by 3
x = 54/3
x = 18
Substitute x = 18 into equation 1
x = y + 8
18 = y + 8
collect like terms
y = 18-8
y = 10
The two numbers are 18 and 10
From the question, One number is 8 more than another
Let the first number be x and the second number be y
∴ x = y + 8 ------ (1)
From the second statement, the sum of the smaller number and twice the larger number is 46
That is,
y + 2x = 46 ----- (2)
Now, we will solve the two equations simultaneously
From equation (1)
We have x = y + 8
Substitute this into equation (2)
y + 2x = 46
y + 2(y+8) = 46
Then, clear the bracket
y + 2y + 16 = 46
3y + 16 = 46
Collect like terms
3y = 46 - 16
3y = 30
∴ y = 30 ÷ 3
y = 10
Substitute the value of y into equation (1)
x = y + 8
x = 10 + 8
x = 18
∴ x = 18 and y = 10
Hence, the two numbers are 18 and 10
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