Question 1. Translate into a variable equation AND solve: Twice the difference between four times a number and five is six. Find the number.
Question 2. Translate each into a variable equation AND solve: The sum of two numbers is two. The difference between eight and twice the smaller number is two less than four times the larger. Find the two numbers.
+130511 1. 2(4n - 5) = 6
Simpify
8n - 10 = 6 add 6 to both sides
8n = 16 divide both sides by 8
n = 2
2. Let x be the first number and y be the second. And we're told that x+ y = 2.... and let x be the smaller number
So
(8-2x) + 2 = 4y ......... (1)
And using x + y = 2 let y = 2-x
So, substituting for y in (1), we have
8-2x + 2 = 4(2-x) simplify
8-2x + 2 = 8 - 4x
10-2x = 8-4x add 4x to each side and subtract 10 from both sides
2x = -2 divide both sides by 2
x = -1
And y = 2 - x = 2-(-1) = 2 + 1 = 3
So, the two numbers are -1 and 3
+130511 1. 2(4n - 5) = 6
Simpify
8n - 10 = 6 add 6 to both sides
8n = 16 divide both sides by 8
n = 2
2. Let x be the first number and y be the second. And we're told that x+ y = 2.... and let x be the smaller number
So
(8-2x) + 2 = 4y ......... (1)
And using x + y = 2 let y = 2-x
So, substituting for y in (1), we have
8-2x + 2 = 4(2-x) simplify
8-2x + 2 = 8 - 4x
10-2x = 8-4x add 4x to each side and subtract 10 from both sides
2x = -2 divide both sides by 2
x = -1
And y = 2 - x = 2-(-1) = 2 + 1 = 3
So, the two numbers are -1 and 3
